35,485 research outputs found
Convex relaxation of mixture regression with efficient algorithms
We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data
An improved \eps expansion for three-dimensional turbulence: two-loop renormalization near two dimensions
An improved \eps expansion in the -dimensional () stochastic
theory of turbulence is constructed at two-loop order which incorporates the
effect of pole singularities at in coefficients of the \eps
expansion of universal quantities. For a proper account of the effect of these
singularities two different approaches to the renormalization of the powerlike
correlation function of the random force are analyzed near two dimensions. By
direct calculation it is shown that the approach based on the mere
renormalization of the nonlocal correlation function leads to contradictions at
two-loop order. On the other hand, a two-loop calculation in the
renormalization scheme with the addition to the force correlation function of a
local term to be renormalized instead of the nonlocal one yields consistent
results in accordance with the UV renormalization theory. The latter
renormalization prescription is used for the two-loop renormalization-group
analysis amended with partial resummation of the pole singularities near two
dimensions leading to a significant improvement of the agreement with
experimental results for the Kolmogorov constant.Comment: 23 pages, 2 figure
Renormalization-group approach to the stochastic Navier--Stokes equation: Two-loop approximation
The field theoretic renormalization group is applied to the stochastic
Navier--Stokes equation that describes fully developed fluid turbulence. The
complete two-loop calculation of the renormalization constant, the
function, the fixed point and the ultraviolet correction exponent is performed.
The Kolmogorov constant and the inertial-range skewness factor, derived to
second order of the \eps expansion, are in a good agreement with the
experiment. The possibility of the extrapolation of the \eps expansion beyond
the threshold where the sweeping effects become important is demonstrated on
the example of a Galilean-invariant quantity, the equal-time pair correlation
function of the velocity field. The extension to the -dimensional case is
briefly discussed.Comment: 20 pages, 3 figure
Anomalous scaling of a passive scalar advected by the Navier--Stokes velocity field: Two-loop approximation
The field theoretic renormalization group and operator product expansion are
applied to the model of a passive scalar quantity advected by a non-Gaussian
velocity field with finite correlation time. The velocity is governed by the
Navier--Stokes equation, subject to an external random stirring force with the
correlation function . It is shown that
the scalar field is intermittent already for small , its structure
functions display anomalous scaling behavior, and the corresponding exponents
can be systematically calculated as series in . The practical
calculation is accomplished to order (two-loop approximation),
including anisotropic sectors. Like for the well-known Kraichnan's rapid-change
model, the anomalous scaling results from the existence in the model of
composite fields (operators) with negative scaling dimensions, identified with
the anomalous exponents. Thus the mechanism of the origin of anomalous scaling
appears similar for the Gaussian model with zero correlation time and
non-Gaussian model with finite correlation time. It should be emphasized that,
in contrast to Gaussian velocity ensembles with finite correlation time, the
model and the perturbation theory discussed here are manifestly Galilean
covariant. The relevance of these results for the real passive advection,
comparison with the Gaussian models and experiments are briefly discussed.Comment: 25 pages, 1 figur
The H molecular ion: a solution
Combining the WKB expansion at large distances and Perturbation Theory at
small distances it is constructed a compact uniform approximation for
eigenfunctions. For lowest states 1s\si_{g} and 2p\si_{u} this
approximation provides the relative accuracy (5 s.d.) for
any real in eigenfunctions and for total energy it gives 10-11 s.d.
for internuclear distances . Corrections to proposed
approximations are evaluated. Separation constants and the oscillator strength
for the transition 1s\si_{g} \rar 2p\si_{u} are calculated and compared with
existing data.Comment: 16 pages, 4 figures, 6 tables, typos are corrected and small
additions are inserted, to be published at JPB (fast track comm
On Prospects for Exploration of Supersymmetry in Double Beta Decay Experiments
We analyze constraints on the parameters of the R-parity violating
supersymmetry which can be extracted from non-observation of the neutrinoless
nuclear double beta decay () at a given half-life lower bound.
Our analysis covers a large class of phenomenologically viable R-parity
violating SUSY models. We introduce special characteristics: the SUSY
sensitivity of a decaying isotope and the SUSY reach of a
experiment. The former provides a physical criterion for a
selection of the most promising isotopes for SUSY searches and the latter gives
a measure of success for a experiment in exploring the
R-parity violating SUSY parameter space. On this basis we discuss prospects for
exploration of supersymmetry in various experiments.Comment: 11 pages, 5 Postscript figures. Modified and updated version is
printed also in Proc. of NANP97 (JINR, Dubna, July 7--11, 1997): Phys. Atom
Nucl, 1998, 61, vol. 6, p.1092--109
A case of Penicillium marneffei osteomyelitis involving the axial skeleton
Fungal infection of bone by Penicillium marneffei is rare. We report on a case of Penicillium marneffei
infection in a Filipino woman, which involved multiple soft-tissue abscesses and infection of the axial
skeleton. Early diagnosis and treatment of this potentially reversible disease is emphasised. Such an
approach is essential to prevent bony destruction from becoming too advanced and, more importantly,
to prevent any damage to the spinal cord from occurring.published_or_final_versio
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