Sum of Us: Strategyproof Selection from the Selectors

We consider directed graphs over a set of n agents, where an edge (i,j) is taken to mean that agent i supports or trusts agent j. Given such a graph and an integer k\leq n, we wish to select a subset of k agents that maximizes the sum of indegrees, i.e., a subset of k most popular or most trusted agents. At the same time we assume that each individual agent is only interested in being selected, and may misreport its outgoing edges to this end. This problem formulation captures realistic scenarios where agents choose among themselves, which can be found in the context of Internet search, social networks like Twitter, or reputation systems like Epinions. Our goal is to design mechanisms without payments that map each graph to a k-subset of agents to be selected and satisfy the following two constraints: strategyproofness, i.e., agents cannot benefit from misreporting their outgoing edges, and approximate optimality, i.e., the sum of indegrees of the selected subset of agents is always close to optimal. Our first main result is a surprising impossibility: for k \in {1,...,n-1}, no deterministic strategyproof mechanism can provide a finite approximation ratio. Our second main result is a randomized strategyproof mechanism with an approximation ratio that is bounded from above by four for any value of k, and approaches one as k grows

Basic Network Creation Games

We study a natural network creation game, in which each node locally tries to minimize its local diameter or its local average distance to other nodes, by swapping one incident edge at a time. The central question is what structure the resulting equilibrium graphs have, in particular, how well they globally minimize diameter. For the local-average-distance version, we prove an upper bound of 2O(√ lg n), a lower bound of 3, a tight bound of exactly 2 for trees, and give evidence of a general polylogarithmic upper bound. For the local-diameter version, we prove a lower bound of Ω(√ n), and a tight upper bound of 3 for trees. All of our upper bounds apply equally well to previously extensively studied network creation games, both in terms of the diameter metric described above and the previously studied price of anarchy (which are related by constant factors). In surprising contrast, our model has no parameter α for the link creation cost, so our results automatically apply for all values of alpha without additional effort; furthermore, equilibrium can be checked in polynomial time in our model, unlike previous models. Our perspective enables simpler and more general proofs that get at the heart of network creation games

Improvement of Mg uptake of grapevine by use of rapeseed oil ethoxylates for foliar application of Mg

To improve the uptake of foliar-applied Mg a new group of toxicological and ecotoxicological harmless surfactants (rapeseed oil ethoxylates) with an average of 5 (Agnique RSO 5®), 10 (Agnique RSO 10®), 30 (Agnique RSO 30®) and 60 (Agnique RSO 60®) units of ethylene oxide (EO) was evaluated as adjuvants for a MgSO4 and Mg(NO3) formulation. The impact of the surfactants on Mg penetration was studied using astomatous cuticular membranes isolated from mature tomato fruit. The biological efficacy of a formulation, containing castor oil, ionic and non-ionic surfactants with and without addition of RSO 5 was investigated in two vineyards at the Moselle valley, cvs Riesling and Regent. Especially RSO 5-surfactant increased Mg penetration through isolated cuticles. Under field conditions, Mg application enhanced significantly the Mg content in leaves. The Mg level in bunch stems merely increased when formulated 'Bittersalz' was applied. 'Magnisal' and formulated 'Magnisal' reduced markedly Mg deficiency symptoms in leaves and increased Mg content in leaves of cv. Regent.

Proving as Fast as Computing: Succinct Arguments with Constant Prover Overhead

Succinct arguments are proof systems that allow a powerful, but untrusted, prover to convince a weak verifier that an input $x$ belongs to a language $L \in NP$, with communication that is much shorter than the $NP$ witness. Such arguments, which grew out of the theory literature, are now drawing immense interest also in practice, where a key bottleneck that has arisen is the high computational cost of \emph{proving} correctness. In this work we address this problem by constructing succinct arguments for general computations, expressed as Boolean circuits (of bounded fan-in), with a \emph{strictly linear} size prover. The soundness error of the protocol is an arbitrarily small constant. Prior to this work, succinct arguments were known with a \emph{quasi-}linear size prover for general Boolean circuits or with linear-size only for arithmetic circuits, defined over large finite fields. In more detail, for every Boolean circuit $C=C(x,w)$, we construct an $O(\log |C|)$-round argument-system in which the prover can be implemented by a size $O(|C|)$ Boolean circuit (given as input both the instance $x$ and the witness $w$), with arbitrarily small constant soundness error and using $poly(\lambda,\log |C|)$ communication, where $\lambda$ denotes the security parameter. The verifier can be implemented by a size $O(|x|) + poly(\lambda, \log |C|)$ circuit following a size $O(|C|)$ private pre-processing step, or, alternatively, by using a purely public-coin protocol (with no pre-processing) with a size $O(|C|)$ verifier. The protocol can be made zero-knowledge using standard techniques (and with similar parameters). The soundness of our protocol is computational and relies on the existence of collision resistant hash functions that can be computed by linear-size circuits, such as those proposed by Applebaum et al. (ITCS, 2017). At the heart of our construction is a new information-theoretic \emph{interactive oracle proof} (IOP), an interactive analog of a PCP, for circuit satisfiability, with constant prover overhead. The improved efficiency of our IOP is obtained by bypassing a barrier faced by prior IOP constructions, which needed to (either explicitly or implicitly) encode the entire computation using a multiplication code

Local Proofs Approaching the Witness Length

Interactive oracle proofs (IOPs) are a hybrid between interactive proofs and PCPs. In an IOP the prover is allowed to interact with a verifier (like in an interactive proof) by sending relatively long messages to the verifier, who in turn is only allowed to query a few of the bits that were sent (like in a PCP). In this work we construct, for a large class of NP relations, IOPs in which the communication complexity approaches the witness length. More precisely, for any NP relation for which membership can be decided in polynomial-time and bounded polynomial space (e.g., SAT, Hamiltonicity, Clique, Vertex-Cover, etc.) and for any constant $\gamma>0$, we construct an IOP with communication complexity $(1+\gamma) \cdot n$, where $n$ is the original witness length. The number of rounds as well as the number of queries made by the IOP verifier are constant. This result improves over prior works on short IOPs/PCPs in two ways. First, the communication complexity in these short IOPs is proportional to the complexity of verifying the NP witness, which can be polynomially larger than the witness size. Second, even ignoring the difference between witness length and non-deterministic verification time, prior works incur (at the very least) a large constant multiplicative overhead to the communication complexity. In particular, as a special case, we also obtain an IOP for Circuit-SAT with rate approaching 1: the communication complexity is $(1+\gamma) \cdot t$, for circuits of size $t$ and any constant $\gamma>0$. This improves upon the prior state-of-the-art work of Ben Sasson et al. (ICALP, 2017) who construct an IOP for CircuitSAT with communication length $c \cdot t$ for a large (unspecified) constant $c \geq 1$. Our proof leverages recent constructions of high-rate locally testable tensor codes. In particular, we bypass the barrier imposed by the low rate of multiplication codes (e.g., Reed-Solomon, Reed-Muller or AG codes) - a core component in all known short PCP/IOP constructions

Structure-dependent optical properties of Au/Ag irradiated TiN thin films

Titanium nitride (TiN) is an attractive alternative for modern and future photonic applications, as its optical properties can be engineered over a wide spectral range. In this study, we have used sequential implantation of gold and silver ions with varying ion fluence, as well as subsequent annealing, in order to modify the optical and plasmonic properties of TiN thin films and correlated this to their structural properties. Our investigations show that the columnar structure of the TiN films is partially destroyed upon implantation, but metallic Au and Ag nanoparticles are formed. The irradiation further induces a reduction of the lattice constant as well as changes the TiN stoichiometry and grain size. From the optical point of view, the implanted films possess less metallicity with increasing Ag fluence and losses several times lower than the as-deposited film, which can be correlated with the deficiency of nitrogen and additional defects. Subsequent annealing partially recovered the destroyed columnar structure, and the films become more metallic where the optical losses are much smaller in comparison to the as-implanted situation, being comparable to those of pure Au and Ag. In this way, by varying the implantation fluence of silver ions properly while keeping the gold fluence constant, we were able to optimize experimental parameters in such a way to ensure the formation of TiN with desirable optical performances

High-energy spectroscopy of YbM2P2 compounds

We have studied experimentally and theoretically the electronic structure and x-ray absorption spectrum at the Yb L3-edge and x-ray emission spectra of M and P at the K- and L2,3 -edges in the mixed valence compound YbM2P2 (with ThCr2Si2 type crystal structure), where M=Fe, Co, Ni. The theoretical calculations have been carried out by means of the ab initio fully-relativistic spin-polarized Dirac linear muffin-tin orbital method. The calculations show good agreement with the experimental measurements. The LSDA +U with Ueff > 8.8 eV produces two independent self-consistent solutions YbNi2P2 with divalent Yb2+ and trivalent Yb3+ ions. For the divalent Yb ion we found a non-magnetic solution with fourteen 4f electron bands completely occupied and situated far below the Fermi level. For trivalent Yb3+ solution thirteen 4f electron bands are situated well below the Fermi level. The hole 4f level for the Yb3+ solution the completely empty and situated sufficiently far from the Fermi level, therefore YbNi2P2 belong to the in homogeneously mixed-valence compounds. The calculated total magnetic moment for the Yb3+ solution moment is dominated by the 4f compounds, the spin Ms and orbital Ml moments are 0.365 μB, and 1.135 μB, respectively. The spin and orbital moments at the Ni and P sites are very small: Ms Ni= - 0.0028 B, MsP=-0.0017 μB, MlNi =-0.0019 μB and MlP =0.0004 μB. Both the trivalent and the divalent Yb ions in are reflected in the experimentally measured Yb L3 x-ray absorption spectrum simultaneously. We found that the best agreement between the experimental spectrum and sum of the theoretically calculated Yb2+ and Yb3+ spectra is achieved with 73% ytterbium ions 2+ state and 27% ions in 3+ state. We found that the effect of the electronic quadrupole E2 transitions as well as the core-hole effect in the final states has minor influence on the intensity and the shape of the Ni and P K and L2.3 emission spectra as well as on the Yb L3 absorption spectrum. We would like to point out that the LSDA +U method which combines LSDA with a basically static, i.e. Hartree-Fock-like, mean –field approximation for a multi-band Anderson lattice model does not contain true many body physics. However, this method can be considered as the first step towards a better description of strongly correlated electron systems. The LSDA +U method provides the correct energy position of 4f energy bands and gives a reasonable description of the XAS and XES properties in YbNi2P2. However, the energy band structure for finite temperatures and the presumed Kondo lattice and mixed valence behavior in YbNi2P2 clearly requires a treatment that goes beyond a static mean-field approximation and includes dynamical effects, e.g., the frequency dependence of the sell-energy

X-ray spectra, electron structure and physical properties of the Ce2ScSi2 and СеScSi compounds

Energy structure of the valence band of the Ce2ScSi2 and СеScSi compounds was studied by the methods of the high-energy spectroscopy (XPS, XES and XAS). Dependence of magnetic susceptibility χ(Т) of the Ce2ScSi2 compound within wide temperature range corresponds to the Curie-Weiss law. Based upon temperature dependences χ(Т) and α(Т), together with calculated valence of Ce by the data of the absorption LІІІ –spectroscopy, a conclusion has been made on the existence of the fluctuating transition, «State of intermediate valence - Condo-systems", in the Ce2ScSi2 compound. The calculations of electron energy bands E(k) and partial DOS for Ce2ScSi2 and СеScSi compounds were performed by the semi relativistic linear muffin-tin orbital method without considerations of spin-orbit interactions A satisfactory agreement between theoretical and experimental data is achieved