1,334 research outputs found
Scattering matrices and Weyl functions
For a scattering system consisting of selfadjoint
extensions and of a symmetric operator with finite
deficiency indices, the scattering matrix \{S_\gT(\gl)\} and a spectral shift
function are calculated in terms of the Weyl function associated
with the boundary triplet for and a simple proof of the Krein-Birman
formula is given. The results are applied to singular Sturm-Liouville operators
with scalar and matrix potentials, to Dirac operators and to Schr\"odinger
operators with point interactions.Comment: 39 page
Trace formulae for dissipative and coupled scattering systems
For scattering systems consisting of a (family of) maximal dissipative
extension(s) and a selfadjoint extension of a symmetric operator with finite
deficiency indices, the spectral shift function is expressed in terms of an
abstract Titchmarsh-Weyl function and a variant of the Birman-Krein formula is
proved.Comment: 38 page
Evaluation of machine learning algorithms for Health and Wellness applications: a tutorial
Research on decision support applications in healthcare, such as those
related to diagnosis, prediction, treatment planning, etc., have seen
enormously increased interest recently. This development is thanks to the
increase in data availability as well as advances in artificial intelligence
and machine learning research. Highly promising research examples are published
daily. However, at the same time, there are some unrealistic expectations with
regards to the requirements for reliable development and objective validation
that is needed in healthcare settings. These expectations may lead to unmet
schedules and disappointments (or non-uptake) at the end-user side. It is the
aim of this tutorial to provide practical guidance on how to assess performance
reliably and efficiently and avoid common traps. Instead of giving a list of
do's and don't s, this tutorial tries to build a better understanding behind
these do's and don't s and presents both the most relevant performance
evaluation criteria as well as how to compute them. Along the way, we will
indicate common mistakes and provide references discussing various topics more
in-depth.Comment: To be published in Computers in Biology and Medicin
Recommended from our members
Trace formulae for dissipative and coupled scattering systems
For scattering systems consisting of a (family of) maximal dissipative
extension(s) and a selfadjoint extension of a symmetric operator with finite
deficiency indices, the spectral shift function is expressed in terms of an
abstract Titchmarsh-Weyl function and a variant of the Birman-Krein formula
is proved
Recommended from our members
Scattering matrices and Weyl functions
For a scattering system consisting of two selfadjoint extensions of a
symmetric operator A with finite deficiency indices, the scattering matrix
and the spectral shift function are calculated in terms of the Weyl function
associated with the boundary triplet for A* and a simple proof of the
Krein-Birman formula is given. The results are applied to singular
Sturm-Liouville operators with scalar- and matrix-valued potentials, to Dirac
operators and to Schroedinger operators with point interactions
Recommended from our members
Finite rank perturbations, scattering matrices and inverse problems : dedicated to the memory of our friend Peter Jonas (18.7.1941 - 18.7.2007)
In this paper the scattering matrix of a scattering system consisting
of two selfadjoint operators with finite dimensional resolvent difference is
expressed in terms of a matrix Nevanlinna function. The problem is embedded
into an extension theoretic framework and the theory of boundary triplets and
associated Weyl functions for (in general nondensely defined) symmetric
operators is applied. The representation results are extended to dissipative
scattering systems and an explicit solution of an inverse scattering problem
for the Lax-Phillips scattering matrix is presented
Expressive Messaging on Mobile Platforms
We present a design for expressive multimodal messaging on mobile platforms. Strong context, simple text messages, and crude animations combine well to produce surprisingly expressive results
Real-Time Closed-Loop Color Control of A Multi-Channel Luminaire Using Sensors Onboard A Mobile Device
Alhaisen 3He/4He suhteen vaippalähde Karoon suuren magmaprovinssin Mg-rikkaimmille magmoille
The massive outpourings of Karoo and Ferrar continental flood basalts (CFBs) ~180 Ma ago mark the initial Jurassic rifting stages of the Gondwana supercontinent. The origin and sources of these eruptions have been debated for decades, largely due to difficulties in defining their parental melt and mantle source characteristics. Recent findings of Fe- and Mg-rich dikes (depleted ferropicrite suite) from Vestfjella, western Dronning Maud Land, Antarctica, have shed light on the composition of the deep sub-Gondwanan mantle: these magmas have been connected to upper mantle sources presently sampled by the Southwest Indian Ocean mid-ocean ridge basalts (SWIR MORBs) or to high 3He/4He plume-entrained non-chondritic primitive mantle sources formed early in Earth’s history. In an attempt to determine their He isotopic composition and relative contributions from magmatic, cosmogenic, and radiogenic He sources, we performed in-vacuo stepwise crushing and melting analyses of olivine mineral separates, some of which were abraded to remove the outer layer. The best estimate for the mantle isotopic composition is given by a sample with the highest amount of He released (> 50%) during the first crushing step of an abraded coarse fraction. It has a 3He/4He of 7.03 ± 0.23 (2σ) times the atmospheric ratio (Ra), which is indistinguishable from those measured from SWIR MORBs (6.3‒7.3 Ra; source 3He/4He ~6.4–7.6 Ra at 180 Ma) and notably lower than in the most primitive lavas from the North Atlantic Igneous Province (up to 50 Ra), considered to represent the epitome magmas from non-chondritic primitive mantle sources. Previously published trace element and isotopic (Sr, Nd, and Pb) compositions do not suggest a direct genetic link to any modern hotspot of Indian or southern Atlantic Oceans. Although influence of a mantle plume cannot be ruled out, the high magma temperatures and SWIR MORB-like geochemistry of the suite are best explained by supercontinent insulation of a precursory Indian Ocean upper mantle source. Such a model is also supported by the majority of the recent studies on the structure, geochronology, and petrology of the Karoo CFBs.The massive outpourings of Karoo and Ferrar continental flood basalts (CFBs) ~180 Ma ago mark the initial Jurassic rifting stages of the Gondwana supercontinent. The origin and sources of these eruptions have been debated for decades, largely due to difficulties in defining their parental melt and mantle source characteristics. Recent findings of Fe- and Mg-rich dikes (depleted ferropicrite suite) from Vestfjella, western Dronning Maud Land, Antarctica, have shed light on the composition of the deep sub-Gondwanan mantle: these magmas have been connected to upper mantle sources presently sampled by the Southwest Indian Ocean mid-ocean ridge basalts (SWIR MORBs) or to high 3He/4He plume-entrained non-chondritic primitive mantle sources formed early in Earth’s history. In an attempt to determine their He isotopic composition and relative contributions from magmatic, cosmogenic, and radiogenic He sources, we performed in-vacuo stepwise crushing and melting analyses of olivine mineral separates, some of which were abraded to remove the outer layer. The best estimate for the mantle isotopic composition is given by a sample with the highest amount of He released (> 50%) during the first crushing step of an abraded coarse fraction. It has a 3He/4He of 7.03 ± 0.23 (2σ) times the atmospheric ratio (Ra), which is indistinguishable from those measured from SWIR MORBs (6.3‒7.3 Ra; source 3He/4He ~6.4–7.6 Ra at 180 Ma) and notably lower than in the most primitive lavas from the North Atlantic Igneous Province (up to 50 Ra), considered to represent the epitome magmas from non-chondritic primitive mantle sources. Previously published trace element and isotopic (Sr, Nd, and Pb) compositions do not suggest a direct genetic link to any modern hotspot of Indian or southern Atlantic Oceans. Although influence of a mantle plume cannot be ruled out, the high magma temperatures and SWIR MORB-like geochemistry of the suite are best explained by supercontinent insulation of a precursory Indian Ocean upper mantle source. Such a model is also supported by the majority of the recent studies on the structure, geochronology, and petrology of the Karoo CFBs.Peer reviewe
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