1,030 research outputs found
Optimal densities of packings consisting of highly unequal objects
Let be the optimal packing density of by unit balls.
We show the optimal packing density using two sizes of balls approaches as the ratio of the radii tends to infinity. More
generally, if is a body and is a finite set of bodies, then the optimal
density of packings consisting of congruent copies of
the bodies from converges to as tends to zero
Moment methods in energy minimization: New bounds for Riesz minimal energy problems
We use moment methods to construct a converging hierarchy of optimization
problems to lower bound the ground state energy of interacting particle
systems. We approximate the infinite dimensional optimization problems in this
hierarchy by block diagonal semidefinite programs. For this we develop the
necessary harmonic analysis for spaces consisting of subsets of another space,
and we develop symmetric sum-of-squares techniques. We compute the second step
of our hierarchy for Riesz -energy problems with five particles on the
-dimensional unit sphere, where the case known as the Thomson problem.
This yields new sharp bounds (up to high precision) and suggests the second
step of our hierarchy may be sharp throughout a phase transition and may be
universally sharp for -particles on . This is the first time a
-point bound has been computed for a continuous problem
Lower bounds on matrix factorization ranks via noncommutative polynomial optimization
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the completely positive rank, and their symmetric analogues: the positive semidefinite rank and the completely positive semidefinite rank. We study the convergence properties of our hierarchies, compare them extensively to known lower bounds, and provide some (numerical) examples
Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization
A platform independent communication library for distributed computing
We present MPWide, a platform independent communication library for performing message passing between supercomputers. Our library couples several local MPI applications through a long distance network using, for example, optical links. The implementation is deliberately kept light-weight, platform independent and the library can be installed and used without administrative privileges. The only requirements are a C++ compiler and at least one open port to a wide area network on each site. In this paper we present the library, describe the user interface, present performance tests and apply MPWide in a large scale cosmological N-body simulation on a network of two computers, one in Amsterdam and the other in Tokyo
ZeroTouch Provisioning (ZTP) Model and Infrastructure Components for Multi-provider Cloud Services Provisioning
Semiquantitative interpretation of anticardiolipin and antiβ2glycoprotein I antibodies measured with various analytical platforms: communication from the ISTH SSC subcommittee on Lupus Anticoagulant/Antiphospholipid antibodies
Background
Antiβ2glycoprotein I (aβ2GPI) and anticardiolipin (aCL) IgG/IgM show differences in positive/negative agreement and titers between solid phase platforms. Method specific semiquantitative categorization of titers could improve and harmonize the interpretation across platforms.
Aim
To evaluate the traditionally 40/80 units thresholds used for aCL and aβ2GPI for categorization into moderate/high positivity with different analytical systems, and to compare with alternative thresholds.
Material and methods
aCL and aβ2GPI thresholds were calculated for two automated systems (chemiluminescent immunoassay (CLIA) and multiplex flow immunoassay (MFI)) by ROC-curve analysis on 1108 patient samples, including patients with and without APS, and confirmed on a second population (n=279). Alternatively, regression analysis on diluted standard material was applied to identify thresholds. Thresholds were compared to 40/80 threshold measured by an enzyme linked immunosorbent assay (ELISA). Additionally, likelihood ratios (LR) were calculated.
Results
Threshold levels of 40/80 units show poor agreement between ELISA and automated platforms for classification into low/moderate/high positivity, especially for aCL/aβ2GPI IgG. Agreement for semiquantitative interpretation of aPL IgG between ELISA and CLIA/MFI improves with alternative thresholds. LR for aPL IgG increase for thrombotic and obstetric APS based on 40/80 thresholds for ELISA and adapted thresholds for the other systems, but not for IgM.
Conclusion
Use of 40/80 units as medium/high thresholds is acceptable for aCL/aβ2GPI IgG ELISA, but not for CLIA and MFI. Alternative semiquantitative thresholds for non-ELISA platforms can be determined by a clinical approach or by using monoclonal antibodies. Semiquantitative reporting of aPL IgM has less impact on increasing probability for APS
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