60 research outputs found
Solving generic nonarchimedean semidefinite programs using stochastic game algorithms
A general issue in computational optimization is to develop combinatorial
algorithms for semidefinite programming. We address this issue when the base
field is nonarchimedean. We provide a solution for a class of semidefinite
feasibility problems given by generic matrices. Our approach is based on
tropical geometry. It relies on tropical spectrahedra, which are defined as the
images by the valuation of nonarchimedean spectrahedra. We establish a
correspondence between generic tropical spectrahedra and zero-sum stochastic
games with perfect information. The latter have been well studied in
algorithmic game theory. This allows us to solve nonarchimedean semidefinite
feasibility problems using algorithms for stochastic games. These algorithms
are of a combinatorial nature and work for large instances.Comment: v1: 25 pages, 4 figures; v2: 27 pages, 4 figures, minor revisions +
benchmarks added; v3: 30 pages, 6 figures, generalization to non-Metzler sign
patterns + some results have been replaced by references to the companion
work arXiv:1610.0674
Gate-tunable, normally-on to normally-off memristance transition inpatterned LaAlO3/SrTiO3 interfaces
The authors gratefully acknowledge the support from the state of Bavaria as well as from the Deutsche Forschungsgemeinschaft (FOR1162 and SFB1170).We report gate-tunable memristive switching in patterned LaAlO3/SrTiO3 interfaces at cryogenic temperatures. The application of voltages in the order of a few volts to the back gate of the device allows controlling and switching on and -off the inherent memory functionality (memristance). For large and small gate voltages a simple non-linear resistance characteristic is observed while a pinched hysteresis loop and memristive switching occurs in an intermediate voltage range. The memristance is further controlled by the density of oxygen vacancies, which is tuned by annealing the sample at 300 °C in nitrogen atmosphere. Depending on the annealing time the memristance at zero gate voltage can be switched on and off leading to normally-on and normally-off memristors. The presented device offers reversible and irreversible control of memristive characteristics by gate voltages and annealing, respectively, which may allow to compensate fabrication variabilities of memristors that complicate the realization of large memristor-based neural networks.PostprintPeer reviewe
Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions
This paper is aimed to show the essential role played by the theory of
quasi-analytic functions in the study of the determinacy of the moment problem
on finite and infinite-dimensional spaces. In particular, the quasi-analytic
criterion of self-adjointness of operators and their commutativity are crucial
to establish whether or not a measure is uniquely determined by its moments.
Our main goal is to point out that this is a common feature of the determinacy
question in both the finite and the infinite-dimensional moment problem, by
reviewing some of the most known determinacy results from this perspective. We
also collect some properties of independent interest concerning the
characterization of quasi-analytic classes associated to log-convex sequences.Comment: 28 pages, Stochastic and Infinite Dimensional Analysis, Chapter 9,
Trends in Mathematics, Birkh\"auser Basel, 201
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