1,672 research outputs found
Nonlinear inverse problem by T-matrix completion. I. Theory
We propose a conceptually new method for solving nonlinear inverse scattering
problems (ISPs) such as are commonly encountered in tomographic ultrasound
imaging, seismology and other applications. The method is inspired by the
theory of nonlocality of physical interactions and utilizes the relevant
formalism. We formulate the ISP as a problem whose goal is to determine an
unknown interaction potential from external scattering data. Although we
seek a local (diagonally-dominated) as the solution to the posed problem,
we allow to be nonlocal at the intermediate stages of iterations. This
allows us to utilize the one-to-one correspondence between and the T-matrix
of the problem, . Here it is important to realize that not every
corresponds to a diagonal and we, therefore, relax the usual condition of
strict diagonality (locality) of . An iterative algorithm is proposed in
which we seek that is (i) compatible with the measured scattering data and
(ii) corresponds to an interaction potential that is as
diagonally-dominated as possible. We refer to this algorithm as to the
data-compatible T-matrix completion (DCTMC). This paper is Part I in a two-part
series and contains theory only. Numerical examples of image reconstruction in
a strongly nonlinear regime are given in Part II. The method described in this
paper is particularly well suited for very large data sets that become
increasingly available with the use of modern measurement techniques and
instrumentation.Comment: This is Part I of a paper series containing theory only. Part II
contains simulations and is available as arXiv:1505.06777 [math-ph]. Accepted
in this form to Phys. Rev.
Solution of the inverse scattering problem by T-matrix completion. II. Simulations
This is Part II of the paper series on data-compatible T-matrix completion
(DCTMC), which is a method for solving nonlinear inverse problems. Part I of
the series contains theory and here we present simulations for inverse
scattering of scalar waves. The underlying mathematical model is the scalar
wave equation and the object function that is reconstructed is the medium
susceptibility. The simulations are relevant to ultrasound tomographic imaging
and seismic tomography. It is shown that DCTMC is a viable method for solving
strongly nonlinear inverse problems with large data sets. It provides not only
the overall shape of the object but the quantitative contrast, which can
correspond, for instance, to the variable speed of sound in the imaged medium.Comment: This is Part II of a paper series. Part I contains theory and is
available at arXiv:1401.3319 [math-ph]. Accepted in this form to Phys. Rev.
Inversion of band-limited discrete Fourier transforms of binary images: Uniqueness and algorithms
Inversion of the two-dimensional discrete Fourier transform (DFT) typically
requires all DFT coefficients to be known. When only band-limited DFT
coefficients of a matrix are known, the original matrix can not be uniquely
recovered. Using a priori information that the matrix is binary (all elements
are either 0 or 1) can overcome the missing high-frequency DFT coefficients and
restore uniqueness. We theoretically investigate the smallest pass band that
can be applied while still guaranteeing unique recovery of an arbitrary binary
matrix. The results depend on the dimensions of the matrix. Uniqueness results
are proven for the dimensions , , and , where are primes numbers and an integer. An
inversion algorithm is proposed for practically recovering the unique binary
matrix. This algorithm is based on integer linear programming methods and
significantly outperforms naive implementations. The algorithm efficiently
reconstructs binary matrices using 81 out of the total 289 DFT
coefficients.Comment: 12 page
Laboratory earthquake forecasting. A machine learning competition
Earthquake prediction, the long-sought holy grail of earthquake science, continues to confound Earth scientists. Could we make advances by crowdsourcing, drawing from the vast knowledge and creativity of the machine learning (ML) community? We used Google’s ML competition platform, Kaggle, to engage the worldwide ML community with a competition to develop and improve data analysis approaches on a forecasting problem that uses laboratory earthquake data. The competitors were tasked with predicting the time remaining before the next earthquake of successive laboratory quake events, based on only a small portion of the laboratory seismic data. The more than 4,500 participating teams created and shared more than 400 computer programs in openly accessible notebooks. Complementing the now well-known features of seismic data that map to fault criticality in the laboratory, the winning teams employed unexpected strategies based on rescaling failure times as a fraction of the seismic cycle and comparing input distribution of training and testing data. In addition to yielding scientific insights into fault processes in the laboratory and their relation with the evolution of the statistical properties of the associated seismic data, the competition serves as a pedagogical tool for teaching ML in geophysics. The approach may provide a model for other competitions in geosciences or other domains of study to help engage the ML community on problems of significance
Quantifying Between-Cohort and Between-Sex Genetic Heterogeneity in Major Depressive Disorder
Major depressive disorder (MDD) is clinically heterogeneous with prevalence rates twice as high in women as in men. There are many possible sources of heterogeneity in MDD most of which are not measured in a sufficiently comparable way across study samples. Here, we assess genetic heterogeneity based on two fundamental measures, between-cohort and between-sex heterogeneity. First, we used genome-wide association study (GWAS) summary statistics to investigate between-cohort genetic heterogeneity using the 29 research cohorts of the Psychiatric Genomics Consortium (PGC; N cases = 16,823, N controls = 25,632) and found that some of the cohort heterogeneity can be attributed to ascertainment differences (such as recruitment of cases from hospital vs community sources). Second, we evaluated between-sex genetic heterogeneity using GWAS summary statistics from the PGC, Kaiser Permanente GERA, UK Biobank and the Danish iPSYCH studies but did not find convincing evidence for genetic differences between the sexes. We conclude that there is no evidence that the heterogeneity between MDD data sets and between sexes reflects genetic heterogeneity. Larger sample sizes with detailed phenotypic records and genomic data remain the key to overcome heterogeneity inherent in assessment of MDD
Search for Yukawa Production of a Light Neutral Higgs Boson at LEP
Within a Two-Higgs-Doublet Model (2HDM) a search for a light Higgs boson in
the mass range of 4-12 GeV has been performed in the Yukawa process e+e- -> b
bbar A/h -> b bbar tau+tau-, using the data collected by the OPAL detector at
LEP between 1992 and 1995 in e+e- collisions at about 91 GeV centre-of-mass
energy. A likelihood selection is applied to separate background and signal.
The number of observed events is in good agreement with the expected
background. Within a CP-conserving 2HDM type II model the cross-section for
Yukawa production depends on xiAd = |tan beta| and xihd = |sin alpha/cos beta|
for the production of the CP-odd A and the CP-even h, respectively, where tan
beta is the ratio of the vacuum expectation values of the Higgs doublets and
alpha is the mixing angle between the neutral CP-even Higgs bosons. From our
data 95% C.L. upper limits are derived for xiAd within the range of 8.5 to 13.6
and for xihd between 8.2 to 13.7, depending on the mass of the Higgs boson,
assuming a branching fraction into tau+tau- of 100%. An interpretation of the
limits within a 2HDM type II model with Standard Model particle content is
given. These results impose constraints on several models that have been
proposed to explain the recent BNL measurement of the muon anomalous magnetic
moment.Comment: 24 pages, 9 figures, Submitted to Euro. Phys. J.
Search for Neutral Higgs Bosons in e+e- Collisions at sqrt(s) ~189GeV
A search for neutral Higgs bosons has been performed with the OPAL detector
at LEP, using approximately 170 pb-1 of e+e- collision data collected at
sqrt(s)~189GeV. Searches have been performed for the Standard Model (SM)
process e+e- to H0Z0 and the MSSM processes e+e- to H0Z0, A0h0. The searches
are sensitive to the b b-bar and tau antitau decay modes of the Higgs bosons,
and also to the MSSM decay mode h0 to A0A0. OPAL search results at lower
centre-of-mass energies have been incorporated in the limits we set, which are
valid at the 95% confidence level. For the SM Higgs boson, we obtain a lower
mass bound of 91.0 GeV. In the MSSM, our limits are mh>74.8GeV and mA>76.5GeV,
assuming tan(beta)>1, that the mixing of the scalar top quarks is either zero
or maximal, and that the soft SUSY-breaking masses are 1 TeV. For the case of
zero scalar top mixing, we exclude values of tan(beta) between 0.72 and 2.19.Comment: 38 pages, 15 figures, submitted Euro. Phys. J.
Bose-Einstein Correlations in e+e- to W+W- at 172 and 183 GeV
Bose-Einstein correlations between like-charge pions are studied in hadronic
final states produced by e+e- annihilations at center-of-mass energies of 172
and 183 GeV. Three event samples are studied, each dominated by one of the
processes W+W- to qqlnu, W+W- to qqqq, or (Z/g)* to qq. After demonstrating the
existence of Bose-Einstein correlations in W decays, an attempt is made to
determine Bose-Einstein correlations for pions originating from the same W
boson and from different W bosons, as well as for pions from (Z/g)* to qq
events. The following results are obtained for the individual chaoticity
parameters lambda assuming a common source radius R: lambda_same = 0.63 +- 0.19
+- 0.14, lambda_diff = 0.22 +- 0.53 +- 0.14, lambda_Z = 0.47 +- 0.11 +- 0.08, R
= 0.92 +- 0.09 +- 0.09. In each case, the first error is statistical and the
second is systematic. At the current level of statistical precision it is not
established whether Bose-Einstein correlations, between pions from different W
bosons exist or not.Comment: 24 pages, LaTeX, including 6 eps figures, submitted to European
Physical Journal
Measurements of Flavour Dependent Fragmentation Functions in Z^0 -> qq(bar) Events
Fragmentation functions for charged particles in Z -> qq(bar) events have
been measured for bottom (b), charm (c) and light (uds) quarks as well as for
all flavours together. The results are based on data recorded between 1990 and
1995 using the OPAL detector at LEP. Event samples with different flavour
compositions were formed using reconstructed D* mesons and secondary vertices.
The \xi_p = ln(1/x_E) distributions and the position of their maxima \xi_max
are also presented separately for uds, c and b quark events. The fragmentation
function for b quarks is significantly softer than for uds quarks.Comment: 29 pages, LaTeX, 5 eps figures (and colour figs) included, submitted
to Eur. Phys. J.
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