Superselectors: Efficient Constructions and Applications

We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel conflict resolution and data security. We prove close upper and lower bounds on the size of superselectors and we provide efficient algorithms for their constructions. Albeit our bounds are very general, when they are instantiated on the combinatorial structures that are particular cases of superselectors (e.g., (p,k,n)-selectors, (d,\ell)-list-disjunct matrices, MUT_k(r)-families, FUT(k, a)-families, etc.) they match the best known bounds in terms of size of the structures (the relevant parameter in the applications). For appropriate values of parameters, our results also provide the first efficient deterministic algorithms for the construction of such structures

High current source of He −

A negative helium ion beam of 70 mA at 10.5 kV has been produced by charge exchange in sodium. The production is studied as a function of sodium line density, beam energy and background helium gas density. The characteristics of this high current He{sup -} source are analyzed to determine the design requirements for He{sup -} beam generation in the range of tens to hundred of milliamperes

Noise-Resilient Group Testing: Limitations and Constructions

We study combinatorial group testing schemes for learning $d$-sparse Boolean vectors using highly unreliable disjunctive measurements. We consider an adversarial noise model that only limits the number of false observations, and show that any noise-resilient scheme in this model can only approximately reconstruct the sparse vector. On the positive side, we take this barrier to our advantage and show that approximate reconstruction (within a satisfactory degree of approximation) allows us to break the information theoretic lower bound of $\tilde{\Omega}(d^2 \log n)$ that is known for exact reconstruction of $d$-sparse vectors of length $n$ via non-adaptive measurements, by a multiplicative factor $\tilde{\Omega}(d)$. Specifically, we give simple randomized constructions of non-adaptive measurement schemes, with $m=O(d \log n)$ measurements, that allow efficient reconstruction of $d$-sparse vectors up to $O(d)$ false positives even in the presence of $\delta m$ false positives and $O(m/d)$ false negatives within the measurement outcomes, for any constant $\delta < 1$. We show that, information theoretically, none of these parameters can be substantially improved without dramatically affecting the others. Furthermore, we obtain several explicit constructions, in particular one matching the randomized trade-off but using $m = O(d^{1+o(1)} \log n)$ measurements. We also obtain explicit constructions that allow fast reconstruction in time \poly(m), which would be sublinear in $n$ for sufficiently sparse vectors. The main tool used in our construction is the list-decoding view of randomness condensers and extractors.Comment: Full version. A preliminary summary of this work appears (under the same title) in proceedings of the 17th International Symposium on Fundamentals of Computation Theory (FCT 2009

First-Principles Evaluation of the Morphology of WS2 Nanotubes for Application as Visible-Light-Driven Water-Splitting Photocatalysts

This study was supported by the EC ERA.Net RUS Plus project No. 237 WATERSPLIT as well as Russian Basic Research Foundation No. 16-53-76019. S.K. and E.S. furthermore gratefully acknowledge computing time granted by the Center for Computational Sciences and Simulation (CCSS) of the Universitaẗ Duisburg-Essen and the supercomputer magnitUDE (DFG grants INST 20876/209-1 FUGG, INST 20876/243-1 FUGG) provided by the Zentrum für Informations-und Mediendienste (ZIM). E.S. is also grateful for support by the Cluster of Excellence RESOLV (EXC1069) funded by the Deutsche Forschungsgemeinschaft.One-dimensional tungsten disulfide (WS2) single-walled nanotubes (NTs) with either achiral, i.e., armchair (n, n) and zigzag-type (n, 0), or chiral (2n, n) configuration with diameters dNT > 1.9 nm have been found to be suitable for photocatalytic applications, since their band gaps correspond to the frequency range of visible light between red and violet (1.5 eV 1.9 nm, the condition ϵVB < ϵO2/H2O < ϵH2/H2O < ϵCB is fulfilled. The values of ϵVB and ϵCB have been found to depend only on the diameter and not on the chirality index of the nanotube. The reported structural and electronic properties have been obtained from either hybrid density functional theory and Hartree-Fock linear combination of atomic orbitals calculations (using the HSE06 functional) or the linear augmented cylindrical waves density functional theory method. In addition to single-walled NTs, we have investigated a number of achiral double-walled (m, m)at(n, n) and (m, 0)at(n, 0) as well as triple-walled (l, l)at(m, m)at(n, n) and (l, 0)at(m, 0)at(n, 0) nanotubes. All multiwalled nanotubes show a common dependence of their band gap on the diameter of the inner nanotube, independent of chirality index and number of walls. This behavior of WS2 NTs allows the exploitation of the entire range of the visible spectrum by suitably tuning the band gap.Deutsche Forschungsgemeinschaft INST 20876/243-1 FUGG,INST 20876/209-1 FUGG,EXC1069; Russian Foundation for Basic Research 16-53-76019; EC ERA.Net RUS Plus project No. 237 WATERSPLIT; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART

New construction of error-tolerant pooling designs

Abstract We present a new class of error-tolerant pooling designs by constructing d z −disjunct matrices associated with subspaces of a finite vector space