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School of Medicine (63) Research Grants Program Office (RGPO) (58) Department of Emergency Medicine (UCI) (12) Sue & Bill Gross School of Nursing (11) Department of Mathematics (5) Department of Psychiatry, UCSD (5)

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Dermatology Online Journal (13) Proceedings of the Annual Meeting of the Cognitive Science Society (13) Western Journal of Emergency Medicine: Integrating Emergency Care with Population Health (12) Proceedings of the Vertebrate Pest Conference (4) California Agriculture (2) California Italian Studies (2)

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## Scholarly Works (724 results)

We review our most recent results on near-IR studies of human brain activity, which have been evolving in two directions: detection of neuronal signals and measurements of functional hemodynamics. We discuss results obtained so far, describing in detail the techniques we developed for detecting neuronal activity, and presenting results of a study that, as we believe, confirms the feasibility of neuronal signal detection. We review our results on near-IR measurements of cerebral hemodynamics, which are performed simultaneously with functional magnetic resonance imaging (MRI) These results confirm the cerebral origin of hemodynamic signals measured by optical techniques on the surface of the head. We also show how near-IR methods can be used to study the underlying physiology of functional MRI signals.

© 2017 Elsevier B.V. We study Riemannian coverings [Formula presented] where M~ is a normal homogeneous space G/K1 fibered over another normal homogeneous space M=G/K and K is locally isomorphic to a nontrivial product K1×K2. The most familiar such fibrations [Formula presented] are the natural fibrations of Stiefel manifolds SO(n1+n2)/SO(n1) over Grassmann manifolds SO(n1+n2)/[SO(n1)×SO(n2)] and the twistor space bundles over quaternionic symmetric spaces (= quaternion-Kaehler symmetric spaces = Wolf spaces). The most familiar of these coverings [Formula presented] are the universal Riemannian coverings of spherical space forms. When M=G/K is reasonably well understood, in particular when G/K is a Riemannian symmetric space or when K is a connected subgroup of maximal rank in G, we show that the Homogeneity Conjecture holds for M~. In other words we show that [Formula presented] is homogeneous if and only if every γ∈Γ is an isometry of constant displacement. In order to find all the isometries of constant displacement on M~ we work out the full isometry group of M~ extending Élie Cartan's determination of the full group of isometries of a Riemannian symmetric space. We also discuss some pseudo-Riemannian extensions of our results.

© 2016, Springer Science+Business Media Dordrecht. Let G be a complex simple direct limit group, specifically SL(∞; C) , SO(∞; C) or Sp(∞; C). Let F be a (generalized) flag in C∞. If G is SO(∞; C) or Sp(∞; C) we suppose further that F is isotropic. Let Z denote the corresponding flag manifold; thus Z= G/ Q where Q is a parabolic subgroup of G. In a recent paper (Penkov and Wolf in Real group orbits on flag ind-varieties of SL∞(C) , to appear in Proceedings in Mathematics and Statistics) we studied real forms G0 of G and properties of their orbits on Z. Here we concentrate on open G0-orbits D⊂ Z. When G0 is of hermitian type we work out the complete G0-orbit structure of flag manifolds dual to the bounded symmetric domain for G0. Then we develop the structure of the corresponding cycle spaces MD. Finally we study the real and quaternionic analogs of these theories. All this extends results from the finite-dimensional cases on the structure of hermitian symmetric spaces and cycle spaces (in chronological order: Wolf in Bull Am Math Soc 75:1121–1237, 1969; Wolf et al. in Ann Math 105:397–448, 1977; Wolf in Ann Math 136:541–555, 1992; Wolf in Compact subvarieties in flag domains, 1994; Wolf and Zierau in Math Ann 316:529–545, 2000; Huckleberry et al. in Journal für die reine und angewandte Mathematik 2001:171–208, 2001; Huckleberry and Wolf in Cycle spaces of real forms of SLn(C) , Springer, New York, pp 111–133, 2002; Wolf and Zierau in J Lie Theory 13:189–191, 2003; Huckleberry and Wolf in Ann Scuola Norm Sup Pisa Cl Sci (5) 9:573-580, 2010).

Recent Work (1982)

In earlier papers we studied direct limits
$${(G,\,K) = \varinjlim\, (G_n,K_n)}$$
of two types of Gelfand pairs. The first type was that in which the G
n
/K
n
are compact Riemannian symmetric spaces. The second type was that in which
$${G_n = N_n\rtimes K_n}$$
with N
n
nilpotent, in other words pairs (G
n
, K
n
) for which G
n
/K
n
is a commutative nilmanifold. In each we worked out a method inspired by the Frobenius–Schur Orthogonality Relations to define isometric injections
$${\zeta_{m,n}: L^2(G_n/K_n) \hookrightarrow L^2(G_m/K_m)}$$
for m ≧ n and prove that the left regular representation of G on the Hilbert space direct limit
$${L^2(G/K) := \varinjlim L^2(G_n/K_n)}$$
is multiplicity-free. This left open questions concerning the nature of the elements of L
2(G/K). Here we define spaces
$${\mathcal{A}(G_n/K_n)}$$
of regular functions on G
n
/K
n
and injections
$${\nu_{m,n} : \mathcal{A}(G_n/K_n) \to \mathcal{A}(G_m/K_m)}$$
for m ≧ n related to restriction by
$${\nu_{m,n}(f)|_{G_n/K_n} = f}$$
. Thus the direct limit
$${\mathcal{A}(G/K) := \varinjlim \{\mathcal{A}(G_n/K_n), \nu_{m,n}\}}$$
sits as a particular G-submodule of the much larger inverse limit
$${\varprojlim \{\mathcal{A}(G_n/K_n), {\rm restriction}\}}$$
. Further, we define a pre Hilbert space structure on
$${\mathcal{A}(G/K)}$$
derived from that of L
2(G/K). This allows an interpretation of L
2(G/K) as the Hilbert space completion of the concretely defined function space
$${\mathcal{A}(G/K)}$$
, and also defines a G-invariant inner product on
$${\mathcal{A}(G/K)}$$
for which the left regular representation of G is multiplicity-free.

The County of San Diego has both "Coastal Sage Scrub" and "Chaparral" in abundance. In fact, these two ecosystems cover most of the ground in the county, albeit with many different types. Many of the plants involved in the two systems are deceptively similar, although they quite commonly belong to different species. Naturally, one would like to know how to keep the two communities apart. The criteria, evidently, are plant species distributions. These have been and are being mapped by various methods, including field work by expert observers, collections of specimens in museum repositories, and the study of air photos and satellite images.

Recent Work (1971)

Recent Work (2000)

Phenomenon of the pseudogap is caused by an intrinsic inhomogeneity and the dependence Tc(r).