1,340 research outputs found
Shintani functions, real spherical manifolds, and symmetry breaking operators
For a pair of reductive groups , we prove a geometric criterion
for the space of Shintani functions to be finite-dimensional
in the Archimedean case.
This criterion leads us to a complete classification of the symmetric pairs
having finite-dimensional Shintani spaces.
A geometric criterion for uniform boundedness of is
also obtained.
Furthermore, we prove that symmetry breaking operators of the restriction of
smooth admissible representations yield Shintani functions of moderate growth,
of which the dimension is determined for .Comment: to appear in Progress in Mathematics, Birkhause
X-ray background and its correlation with the 21 cm signal
We use high resolution hydrodynamical simulations to study the contribution
to the X-ray background from high- energetic sources, such as X-ray
binaries, accreting nuclear black holes and shock heated interstellar medium.
Adopting the model discussed in Eide et al. (2018), we find that these X-ray
sources during the Epoch of Reionization (EoR) contribute less than a few
percent of the unresolved X-ray background. The same sources contribute to less
than 2\% of the measured angular power spectrum of the fluctuations of
the X-ray background. The outputs of radiative transfer simulations modeling
the EoR are used to evaluate the cross-correlations of X-ray background with
the 21~cm signal from neutral hydrogen. Such correlation could be used to
confirm the origin of the 21 cm signal, as well as give information on the
properties of the X-ray sources during the EoR. We find that the correlations
are positive during the early stages of reionization when most of the hydrogen
is neutral, while they become negative when the intergalactic medium gets
highly ionized, with the transition from positive to negative depending on both
the X-ray model and the scale under consideration. With {\tt SKA} as the
reference instrument for the 21~cm experiment, the predicted S/N for such
correlations is if the corresponding X-ray survey is only able to resolve
and remove X-ray sources with observed flux , while the cumulative S/N from to at
is if sources with observed flux are detected.Comment: 9 pages, 8 figure
OPENING PANDORA’S JURY BOX
More than sixty years ago, the U.S. Supreme Court decided Remmer v. United States, thereby defining what procedural steps restore a defendant’s Sixth Amendment right to a fair trial in the face of a contaminated or partial jury. Remmer, a case replete with evidence of jury tampering and covert investigations, fashioned the remedy for future courts to redress allegations of jury taint. Upon making out a prima facie case, a defendant is entitled to an evidentiary hearing, at which the evidence is presumed to prejudice the defendant, and the government bears the burden of rebutting. In Remmer’s wake, however, the Court issued two subsequent opinions that some circuits have interpreted to obviate the presumption of prejudice and restrict Remmer’s rule. This Note observes the inconsistent effects of the current circuit split on defendants’ rights at trial, and it contends that the disparity will increase as technology dissolves access barriers between jurors and outside information. This Note examines where Supreme Court jurisprudence, circuit procedure, and habeas corpus doctrine have shaped the current circuit split. It then proposes that circuits can mend the split and pave a unified path forward by reframing their analyses to include three additional considerations. Further, by separating allegations of jury taint into three subcategories, circuits can renew Remmer’s pretechnology rule to properly address jury taint in a digital age
Eigenfunctions of the Laplacian and associated Ruelle operator
Let be a co-compact Fuchsian group of isometries on the Poincar\'e
disk \DD and the corresponding hyperbolic Laplace operator. Any
smooth eigenfunction of , equivariant by with real
eigenvalue , where , admits an integral
representation by a distribution \dd_{f,s} (the Helgason distribution) which
is equivariant by and supported at infinity \partial\DD=\SS^1. The
geodesic flow on the compact surface \DD/\Gamma is conjugate to a suspension
over a natural extension of a piecewise analytic map T:\SS^1\to\SS^1, the
so-called Bowen-Series transformation. Let be the complex Ruelle
transfer operator associated to the jacobian . M. Pollicott showed
that \dd_{f,s} is an eigenfunction of the dual operator for the
eigenvalue 1. Here we show the existence of a (nonzero) piecewise real analytic
eigenfunction of for the eigenvalue 1, given by an
integral formula \psi_{f,s} (\xi)=\int \frac{J(\xi,\eta)}{|\xi-\eta|^{2s}}
\dd_{f,s} (d\eta), \noindent where is a -valued
piecewise constant function whose definition depends upon the geometry of the
Dirichlet fundamental domain representing the surface \DD/\Gamma
On Kostant's partial order on hyperbolic elements
We study Kostant's partial order on the elements of a semisimple Lie group in
relations with the finite dimensional representations. In particular, we prove
the converse statement of [3, Theorem 6.1] on hyperbolic elements.Comment: 7 page
Measuring patchy reionisation with kSZ-21 cm correlations
We study cross-correlations of the kinetic Sunyaev-Zel'dovich effect (kSZ)
and 21 cm signals during the epoch of reionisation (EoR) to measure the effects
of patchy reionisation. Since the kSZ effect is proportional to the
line-of-sight velocity, the kSZ-21 cm cross correlation suffers from
cancellation at small angular scales. We thus focus on the correlation between
the kSZ-squared field (kSZ) and 21 cm signals. When the global ionisation
fraction is low (), the kSZ fluctuation is dominated by
rare ionised bubbles which leads to an anti-correlation with the 21 cm signal.
When , the correlation is dominated by small pockets of
neutral regions, leading to a positive correlation. However, at very high
redshifts when , the spin temperature fluctuations change the sign of
the correlation from negative to positive, as weakly ionised regions can have
strong 21 cm signals in this case. To extract this correlation, we find that
Wiener filtering is effective in removing large signals from the primary CMB
anisotropy. The expected signal-to-noise ratios for a 10-hour integration
of upcoming Square Kilometer Array data cross-correlated with maps from the
current generation of CMB observatories with 3.4~K arcmin noise and
1.7~arcmin beam over 100~deg are 51, 60, and 37 for , 0.5, and
0.9, respectively.Comment: 7pages, 7 figure
Differences in soil microbial communities in organic and conventional management systems alter soil nutrient dynamics
Non-Peer Reviewe
Medical concepts related to individual risk are better explained with "plausibility" rather than "probability"
BACKGROUND: The concept of risk has pervaded medical literature in the last decades and has become a familiar topic, and the concept of probability, linked to binary logic approach, is commonly applied in epidemiology and clinical medicine. The application of probability theory to groups of individuals is quite straightforward but can pose communication challenges at individual level. Few articles by the way have tried to focus the concept of "risk" at the individual subject level rather than at population level. DISCUSSION: The author has reviewed the conceptual framework which has led to the use of probability theory in the medical field in a time when the principal causes of death were represented by acute disease often of infective origin. In the present scenario, in which chronic degenerative disease dominate and there are smooth transitions between health and disease the use of fuzzy logic rather than binary logic would be more appropriate. The use of fuzzy logic in which more than two possible truth-value assignments are allowed overcomes the trap of probability theory when dealing with uncertain outcomes, thereby making the meaning of a certain prognostic statement easier to understand by the patient. SUMMARY: At individual subject level the recourse to the term plausibility, related to fuzzy logic, would help the physician to communicate to the patient more efficiently in comparison with the term probability, related to binary logic. This would represent an evident advantage for the transfer of medical evidences to individual subjects
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