12,671 research outputs found
Wormwholes: A Commentary On K.F. Schaffer\u27s Genes, Behavior, And Developmental Emergentism
Although Caenorhabditis elegans was chosen and modified to be an organism that would facilitate a reductionist program for neurogenetics, recent research has provided evidence for properties that are emergent from the neurons. While neurogenetic advances have been made using C. elegans which may be useful in explaining human neurobiology, there are severe limitations on C. elegans to explain any significant human behavior
Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives
We consider the problem of finding commuting self-adjoint extensions of the
partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain
C_c^\infty(\Omega) where the self-adjointness is defined relative to
L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is
Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E.
Segal and B. Fuglede, and is difficult in general. In this paper, we provide a
representation-theoretic answer in the special case when \Omega=I\times\Omega_2
and I is an open interval. We then apply the results to the case when \Omega is
a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that
{e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal
basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km,
02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt,
61.44.B
Generalized CMB initial conditions with pre-equality magnetic fields
The most general initial conditions of CMB anisotropies, compatible with the
presence of pre-equality magnetic fields, are derived. When the plasma is
composed by photons, baryons, electrons, CDM particles and neutrinos, the
initial data of the truncated Einstein-Boltzmann hierarchy contemplate one
magnetized adiabatic mode and four (magnetized) non-adiabatic modes. After
obtaining the analytical form of the various solutions, the Einstein-Boltzmann
hierarchy is numerically integrated for the corresponding sets of initial data.
The TT, TE and EE angular power spectra are illustrated and discussed for the
magnetized generalization of the CDM-radiation mode, of the baryon-radiation
mode and of the non-adiabatic mode of the neutrino sector. Mixtures of initial
conditions are examined by requiring that the magnetized adiabatic mode
dominates over the remaining non-adiabatic contributions. In the latter case,
possible degeneracies between complementary sets of initial data might be
avoided through the combined analysis of the TT, TE and EE angular power
spectra at high multipoles (i.e. ).Comment: 28 pages, 24 included figures in eps styl
Harmonic analysis of iterated function systems with overlap
In this paper we extend previous work on IFSs without overlap. Our method
involves systems of operators generalizing the more familiar Cuntz relations
from operator algebra theory, and from subband filter operators in signal
processing.Comment: 37 page
Wavelets in mathematical physics: q-oscillators
We construct representations of a q-oscillator algebra by operators on Fock
space on positive matrices. They emerge from a multiresolution scaling
construction used in wavelet analysis. The representations of the Cuntz Algebra
arising from this multiresolution analysis are contained as a special case in
the Fock Space construction.Comment: (03/11/03):18 pages; LaTeX2e, "article" document class with
"letterpaper" option An outline was added under the abstract (p.1),
paragraphs added to Introduction (p.2), mat'l added to Proofs in Theorems 1
and 6 (pgs.5&17), material added to text for the conclusion (p.17), one add'l
reference added [12]. (04/22/03):"number 1" replace with "term C" (p.9),
single sentences reformed into a one paragraph (p.13), QED symbol moved up
one paragraph and last paragraph labeled as "Concluding Remarks.
Charge exchange contribution to the decay of the ring current, measured by energetic neutral atoms (ENAs)
In this paper we calculate the contribution of charge exchange to the decay of the ring current. Past works have suggested that charge exchange of ring current protons is primarily responsible for the decay of the ring current during the late recovery phase, but there is still much debate about the fast decay of the early recovery phase. We use energetic neutral atom (ENA) measurements from Polar to calculate the total ENA energy escape. To get the total ENA escape we apply a forward modeling technique, and to estimate the total ring current energy escape we use the Dessler-Parker-Sckopke relationship. We find that during the late recovery phase of the March 10, 1998 storm ENAs with energies greater than 17.5 keV can account for 75% of the estimated energy loss from the ring current. During the fast recovery the measured ENAs can only account for a small portion of the total energy loss. We also find that the lifetime of the trapped ions is significantly shorter during the fast recovery phase than during the late recovery phase, suggesting that different processes are operating during the two phases
Observations of nitrogen isotope fractionation in deeply embedded protostars
(Abridged) The terrestrial planets, comets, and meteorites are significantly
enriched in 15N compared to the Sun and Jupiter. While the solar and jovian
nitrogen isotope ratio is believed to represent the composition of the
protosolar nebula, a still unidentified process has caused 15N-enrichment in
the solids. Several mechanisms have been proposed to explain the variations,
including chemical fractionation. However, observational results that constrain
the fractionation models are scarce. While there is evidence of 15N-enrichment
in prestellar cores, it is unclear how the signature evolves into the
protostellar phases. Our aim is to measure the 14N/15N ratio around three
nearby, embedded low-to-intermediate-mass protostars. Isotopologues of HCN and
HNC were used to probe the 14N/15N ratio. A selection of H13CN, HC15N, HN13C,
and H15NC transitions was observed with the APEX telescope. The 14N/15N ratios
were derived from the integrated intensities assuming a standard 12C/13C ratio.
The assumption of optically thin emission was verified using radiative transfer
modeling and hyperfine structure fitting. Two sources, IRAS 16293A and R CrA
IRS7B, show 15N-enrichment by a factor of around 1.5-2.5 in both HCN and HNC
with respect to the solar composition. Solar composition cannot be excluded for
the third source, OMC-3 MMS6. Furthermore, there are indications of a trend
toward increasing 14N/15N ratios with increasing outer envelope temperature.
The enhanced 15N abundances in HCN and HNC found in two Class~0 sources
(14N/15N of 160-290) and the tentative trend toward a temperature-dependent
14N/15N ratio are consistent with the chemical fractionation scenario, but
14N/15N ratios from additional tracers are indispensable for testing the
models. Spatially resolved observations are needed to distinguish between
chemical fractionation and isotope-selective photochemistry.Comment: Accepted for publication in Astronomy and Astrophysics. 16 pages, 13
figure
An extension of Wiener integration with the use of operator theory
With the use of tensor product of Hilbert space, and a diagonalization
procedure from operator theory, we derive an approximation formula for a
general class of stochastic integrals. Further we establish a generalized
Fourier expansion for these stochastic integrals. In our extension, we
circumvent some of the limitations of the more widely used stochastic integral
due to Wiener and Ito, i.e., stochastic integration with respect to Brownian
motion. Finally we discuss the connection between the two approaches, as well
as a priori estimates and applications.Comment: 13 page
Analysis of unbounded operators and random motion
We study infinite weighted graphs with view to \textquotedblleft limits at
infinity,\textquotedblright or boundaries at infinity. Examples of such
weighted graphs arise in infinite (in practice, that means \textquotedblleft
very\textquotedblright large) networks of resistors, or in statistical
mechanics models for classical or quantum systems. But more generally our
analysis includes reproducing kernel Hilbert spaces and associated operators on
them. If is some infinite set of vertices or nodes, in applications the
essential ingredient going into the definition is a reproducing kernel Hilbert
space; it measures the differences of functions on evaluated on pairs of
points in . And the Hilbert norm-squared in will represent
a suitable measure of energy. Associated unbounded operators will define a
notion or dissipation, it can be a graph Laplacian, or a more abstract
unbounded Hermitian operator defined from the reproducing kernel Hilbert space
under study. We prove that there are two closed subspaces in reproducing kernel
Hilbert space which measure quantitative notions of limits at
infinity in , one generalizes finite-energy harmonic functions in
, and the other a deficiency index of a natural operator in
associated directly with the diffusion. We establish these
results in the abstract, and we offer examples and applications. Our results
are related to, but different from, potential theoretic notions of
\textquotedblleft boundaries\textquotedblright in more standard random walk
models. Comparisons are made.Comment: 38 pages, 4 tables, 3 figure
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