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We consider distributed iterative algorithms for the averaging problem over timevarying topologies. Our focus is on the convergence time of such algorithms when complete (unquantized) information is available, and on the degradation of performance when only quantized information is available. We study a large and natural class of averaging algorithms, which includes the vast majority of algorithms proposed to date, and provide tight polynomial bounds on their convergence time. We also describe an algorithm within this class whose convergence time is the best among currently available averaging algorithms for time-varying topologies. We then propose and analyze distributed averaging algorithms under the additional constraint that agents can only store and communicate quantized information, so that they can only converge to the average of the initial values of the agents within some error. We establish bounds on the error and tight bounds on the convergence time, as a function of the number of quantization levels. *

Given a linear system, we consider the problem of finding a small set of variables to affect with an input so that the resulting system is controllable. We show that this problem is NP-hard; indeed, we show that even approximating the minimum number of variables that need to be affected within a multiplicative factor of c log n is NP-hard for some positive c. On the positive side, we show it is possible to find sets of variables matching this inapproximability barrier in polynomial time. This can be done by a simple greedy heuristic which sequentially picks variables to maximize the rank increase of the controllability matrix. Experiments on Erdos-Renyi random graphs demonstrate this heuristic almost always succeeds at findings the minimum number of variables.1 One may also consider variations in which we search for a matrix B ′ ∈ R n×n renderingẋ = Ax + B ′ u controllable while seeking to minimize either the number of nonzero entries of B ′ , or the number of rows of B ′ with a nonzero entry (representing the number of components of the system affected). However, for any such matrix B ′ , we can easily construct a diagonal matrix B rendering the system controllable without increasing the number of nonzero entries, or the number of rows with a nonzero entry: indeed, if the i'th row of B ′ contains a nonzero entry, we simply set Bii = 1, and else we set Bii = 0. Consequently, both of these variations are easily seen to be equivalent to the problem of finding the sparsest diagonal matrix.

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DANSS is a highly segmented 1 m 3 plastic scintillator detector. Its 2500 one meter long scintillator strips have a Gdloaded reflective cover. The DANSS detector is placed under an industrial 3.1 GW th reactor of the Kalinin Nuclear Power Plant 350 km NW from Moscow. The distance to the core is varied on-line from 10.7 m to 12.7 m. The reactor building provides about 50 m water-equivalent shielding against the cosmic background. DANSS detects almost 5000 ν e per day at the closest position with the cosmic background less than 3%. The inverse beta decay process is used to detectν e . Sterile neutrinos are searched for assuming the 4ν model (3 active and 1 sterile ν). The exclusion area in the ∆m 2 14 , sin 2 2θ 14 plane is obtained using a ratio of positron energy spectra collected at different distances. Therefore results do not depend on the shape and normalization of the reactorν e spectrum, as well as on the detector efficiency. Results are based on 966 thousand antineutrino events collected at three different distances from the reactor core. The excluded area covers a wide range of the sterile neutrino parameters up to sin 2 2θ 14 < 0.01 in the most sensitive region.Published in the Phys.Lett.B as

The first measurement of transverse-spin-dependent azimuthal asymmetries in the pion-induced Drell-Yan (DY) process is reported. We use the CERN SPS 190  GeV/c π^{-} beam and a transversely polarized ammonia target. Three azimuthal asymmetries giving access to different transverse-momentum-dependent (TMD) parton distribution functions (PDFs) are extracted using dimuon events with invariant mass between 4.3  GeV/c^{2} and 8.5  GeV/c^{2}. Within the experimental uncertainties, the observed sign of the Sivers asymmetry is found to be consistent with the fundamental prediction of quantum chromodynamics (QCD) that the Sivers TMD PDFs extracted from DY have a sign opposite to the one extracted from semi-inclusive deep-inelastic scattering (SIDIS) data. We present two other asymmetries originating from the pion Boer-Mulders TMD PDFs convoluted with either the nucleon transversity or pretzelosity TMD PDFs. A recent COMPASS SIDIS measurement was obtained at a hard scale comparable to that of these DY results. This opens the way for possible tests of fundamental QCD universality predictions.

We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves a problem that has been open since 1992 when N. Z. Shor asked for the complexity of deciding convexity for quartic polynomials. We also prove that deciding strict convexity, strong convexity, quasiconvexity, and pseudoconvexity of polynomials of even degree four or higher is strongly NP-hard. By contrast, we show that quasiconvexity and pseudoconvexity of odd degree polynomials can be decided in polynomial time.

Abstract-We consider a convex unconstrained optimization problem that arises in a network of agents whose goal is to cooperatively optimize the sum of the individual agent objective functions through local computations and communications. For this problem, we use averaging algorithms to develop distributed subgradient methods that can operate over a timevarying topology. Our focus is on the convergence rate of these methods and the degradation in performance when only quantized information is available. Based on our recent results on the convergence time of distributed averaging algorithms, we derive improved upper bounds on the convergence rate of the unquantized subgradient method. We then propose a distributed subgradient method under the additional constraint that agents can only store and communicate quantized information, and we provide bounds on its convergence rate that highlight the dependence on the number of quantization levels.