Differentially Private Distributed Optimization

In distributed optimization and iterative consensus literature, a standard problem is for $N$ agents to minimize a function $f$ over a subset of Euclidean space, where the cost function is expressed as a sum $\sum f_i$. In this paper, we study the private distributed optimization (PDOP) problem with the additional requirement that the cost function of the individual agents should remain differentially private. The adversary attempts to infer information about the private cost functions from the messages that the agents exchange. Achieving differential privacy requires that any change of an individual's cost function only results in unsubstantial changes in the statistics of the messages. We propose a class of iterative algorithms for solving PDOP, which achieves differential privacy and convergence to the optimal value. Our analysis reveals the dependence of the achieved accuracy and the privacy levels on the the parameters of the algorithm. We observe that to achieve $\epsilon$-differential privacy the accuracy of the algorithm has the order of $O(\frac{1}{\epsilon^2})$

Synchronization transition of heterogeneously coupled oscillators on scale-free networks

We investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent $\lambda$. An oscillator of degree $k_i$ is coupled to its neighboring oscillators with asymmetric and degree-dependent coupling in the form of \couplingcoeff k_i^{\eta-1}. By invoking the mean-field approach, we determine the synchronization transition point $J_c$, which is zero (finite) when $\eta > \lambda-2$ ($\eta < \lambda-2$). We find eight different synchronization transition behaviors depending on the values of $\eta$ and $\lambda$, and derive the critical exponents associated with the order parameter and the finite-size scaling in each case. The synchronization transition is also studied from the perspective of cluster formation of synchronized vertices. The cluster-size distribution and the largest cluster size as a function of the system size are derived for each case using the generating function technique. Our analytic results are confirmed by numerical simulations.Comment: 11 pages, 3 figures and two table

Acoustic power absorption and enhancement generated by slow and fast MHD waves

We used long duration, high quality, unresolved (Sun-as-a star) observations collected by the ground based network BiSON and by the instruments GOLF and VIRGO on board the ESA/NASA SOHO satellite to search for solar-cycle-related changes in mode characteristics in velocity and continuum intensity for the frequency range between 2.5mHz < nu < 6.8mHz. Over the ascending phase of solar cycle 23 we found a suppression in the p-mode amplitudes both in the velocity and intensity data between 2.5mHz <nu< 4.5mHz with a maximum suppression for frequencies in the range between 2.5mHz <nu< 3.5mHz. The size of the amplitude suppression is 13+-2 per cent for the velocity and 9+-2 per cent for the intensity observations. Over the range 4.5mHz <nu< 5.5mHz the findings hint within the errors to a null change both in the velocity and intensity amplitudes. At still higher frequencies, in the so called High-frequency Interference Peaks (HIPs) between 5.8mHz <nu < 6.8mHz, we found an enhancement in the velocity amplitudes with the maximum 36+-7 per cent occurring for 6.3mHz <nu< 6.8mHz. However, in intensity observations we found a rather smaller enhancement of about 5+-2 per cent in the same interval. There is evidence that the frequency dependence of solar-cycle velocity amplitude changes is consistent with the theory behind the mode conversion of acoustic waves in a non-vertical magnetic field, but there are some problems with the intensity data, which may be due to the height in the solar atmosphere at which the VIRGO data are taken.Comment: Accepted for publication in A&A. 10 pages, 9 figures

Application of Near Infrared Reflectance Spectroscopy (NIRS) to Forage Evaluation in Uruguay

Near infrared reflectance spectroscopy (NIRS) were used to assess the chemical composition of a wide range of forages. Nearly five hundred herbage samples covering a wide range of temperate pastures species and mixtures, previously analysed by conventional wet chemistry were scanned in reflectance with a NIRS 6500 (NIRSystems, Silver Spring, USA). The coefficients of determination in calibration (R2 ) and the errors in cross validation (SECV) were 0.98 (5.8), 0.94 (22.2), 0.97 (5.6), 0.94 (6.9) and 0.89 (19.7) for crude protein, in vitro organic matter digestibility, dry matter, ash and acid detergent fiber, in g kg –1 on a dry weight respectively. The high correlation between NIRS and chemical analysis found in this study showed the potential use of NIRS for prediction forage quality

QED Corrections to the Scattering of Solar Neutrinos and Electrons

We discuss recent calculations of the O(alpha) QED corrections to the recoil electron energy spectrum in neutrino electron scattering, and to the spectrum of the combined energy of the recoil electron and a possible accompanying photon emitted in the scattering process. We then examine the role of these corrections in the interpretation of precise measurements from solar neutrino electron scattering experiments.Comment: (16 Pages, 4 Figures) Presented at the Symposium in Honor of Professor Alberto Sirlin's 70th Birthday: ``50 Years of Precision Electroweak Physics'', New York University, October 27-28, 200

Uncertainties of predictions in models of eternal inflation

In a previous paper \cite{MakingPredictions}, a method of comparing the volumes of thermalized regions in eternally inflating universe was introduced. In this paper, we investigate the dependence of the results obtained through that method on the choice of the time variable and factor ordering in the diffusion equation that describes the evolution of eternally inflating universes. It is shown, both analytically and numerically, that the variation of the results due to factor ordering ambiguity inherent in the model is of the same order as their variation due to the choice of the time variable. Therefore, the results are, within their accuracy, free of the spurious dependence on the time parametrization.Comment: 30 pages, RevTeX, figure included, added some references and Comments on recent proposal (gr-qc/9511058) of alternative regularization schemes, to appear in Phys. Rev.

Matrix Product State and mean field solutions for one-dimensional systems can be found efficiently

We consider the problem of approximating ground states of one-dimensional quantum systems within the two most common variational ansatzes, namely the mean field ansatz and Matrix Product States. We show that both for mean field and for Matrix Product States of fixed bond dimension, the optimal solutions can be found in a way which is provably efficient (i.e., scales polynomially). This implies that the corresponding variational methods can be in principle recast in a way which scales provably polynomially. Moreover, our findings imply that ground states of one-dimensional commuting Hamiltonians can be found efficiently.Comment: 5 pages; v2: accepted version, Journal-ref adde

Bloomery iron smelting in the Daye County (Hubei): Technological traditions in Qing China

China is widely accepted as the birthplace and shrine of the blast furnace, with bloomery iron technology largely believed to be scant before the Han Dynasty, and virtually inexistent afterwards. Challenging this traditional picture, this paper presents the material characterisation and reverse engineering of the primary smelting of bloomery iron at five metal production sites, located in close proximity of each other in the Daye County in Hubei Province, China, and in operation during the middle Qing Dynasty. A combination of materials science analyses–optical microscopy, SEM-EDS and WD-XRF–of surface collected technical material such as slags, furnace remains, and ores has demonstrated the established existence of bloomery iron at the core of the Chinese Empire. The five case studies present robust evidence of an overall broadly shared technical procedure based on the smelting of high grade ores in batteries of embanked furnaces, generating abundant slag but a limited metal output. The reconstruction of the various smelting processes in a relatively small region illustrates different technological adaptations to natural resources and socio-technological contexts, which are discussed using conceptual frameworks of rational economy and technological traditions.This paper is based on the PhD dissertation undertaken by David Larreina-Garcia at the UCL Institute of Archaeology, under the primary supervision of Marcos Martinón-Torres, carried out with the financial support of a UCL Impact Scholarship funded by UCL, the Institute for Archaeo-Metallurgical Studies (IAMS) and the Rio Tinto Group. Radiocarbon dates were obtained through the NERC/AHRC radiocarbon service (grant n° NF/2014/2/12)