The Networked Common Goods Game

We introduce a new class of games called the networked common goods game (NCGG), which generalizes the well-known common goods game. We focus on a fairly general subclass of the game where each agent's utility functions are the same across all goods the agent is entitled to and satisfy certain natural properties (diminishing return and smoothness). We give a comprehensive set of technical results listed as follows. * We show the optimization problem faced by a single agent can be solved efficiently in this subclass. The discrete version of the problem is however NP-hard but admits an fully polynomial time approximation scheme (FPTAS). * We show uniqueness results of pure strategy Nash equilibrium of NCGG, and that the equilibrium is fully characterized by the structure of the network and independent of the choices and combinations of agent utility functions. * We show NCGG is a potential game, and give an implementation of best/better response Nash dynamics that lead to fast convergence to an $\epsilon$-approximate pure strategy Nash equilibrium. * Lastly, we show the price of anarchy of NCGG can be as large as $\Omega(n^{1-\epsilon})$ (for any $\epsilon>0$), which means selfish behavior in NCGG can lead to extremely inefficient social outcomes

Strong duality in conic linear programming: facial reduction and extended duals

The facial reduction algorithm of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program $$(P) \sup {<c, x> | Ax \leq_K b}$$ in the absence of any constraint qualification. The facial reduction algorithm solves a sequence of auxiliary optimization problems to obtain such a dual. Ramana's dual is applicable when (P) is a semidefinite program (SDP) and is an explicit SDP itself. Ramana, Tuncel, and Wolkowicz showed that these approaches are closely related; in particular, they proved the correctness of Ramana's dual using certificates from a facial reduction algorithm. Here we give a clear and self-contained exposition of facial reduction, of extended duals, and generalize Ramana's dual: -- we state a simple facial reduction algorithm and prove its correctness; and -- building on this algorithm we construct a family of extended duals when $K$ is a {\em nice} cone. This class of cones includes the semidefinite cone and other important cones.Comment: A previous version of this paper appeared as "A simple derivation of a facial reduction algorithm and extended dual systems", technical report, Columbia University, 2000, available from http://www.unc.edu/~pataki/papers/fr.pdf Jonfest, a conference in honor of Jonathan Borwein's 60th birthday, 201

Noise reduction in 3D noncollinear parametric amplifier

We analytically find an approximate Bloch-Messiah reduction of a noncollinear parametric amplifier pumped with a focused monochromatic beam. We consider type I phase matching. The results are obtained using a perturbative expansion and scaled to a high gain regime. They allow a straightforward maximization of the signal gain and minimization of the parametric fluorescence noise. We find the fundamental mode of the amplifier, which is an elliptic Gaussian defining the optimal seed beam shape. We conclude that the output of the amplifier should be stripped of higher order modes, which are approximately Hermite-Gaussian beams. Alternatively, the pump waist can be adjusted such that the amount of noise produced in the higher order modes is minimized.Comment: 18 pages, 9 figures, accepted to Applied Physics

1/N_c- expansion of the quark condensate at finite temperature

Previously the quark and meson properties in a many quark system at finite temperature have been studied within effective QCD approaches in the Hartree approximation. In the present paper we consider the influence of the mesonic correlations on the quark self-energy and on the quark propagator within a systematic $1/N_c$- expansion. Using a general separable ansatz for the nonlocal interaction, we derive a selfconsistent equation for the $1/N_c$ correction to the quark propagator. For a separable model with cut-off formfactor, we obtain a decrease of the condensate of the order of 20\% at zero temperature. A lowering the critical temperature for the onset of the chiral restoration transition due to the inclusion of mesonic correlations is obtained what seems to be closer to the results from lattice calculations.Comment: 19 pages, REVTeX, 5 figure

Participant acceptability of digital footprint data collection strategies:an exemplar approach to participant engagement and involvement in the ALSPAC birth cohort study

INTRODUCTION: Digital footprint records – the tracks and traces amassed by individuals as a result of their interactions with the internet, digital devices and services – can provide ecologically valid data on individual behaviours. These could enhance longitudinal population study databanks; but few UK longitudinal studies are attempting this. When using novel sources of data, study managers must engage with participants in order to develop ethical data processing frameworks that facilitate data sharing whilst safeguarding participant interests. OBJECTIVES: This paper aims to summarise the participant involvement approach used by the ALSPAC birth cohort study to inform the development of a framework for using linked participant digital footprint data, and provide an exemplar for other data linkage infrastructures. METHODS: The paper synthesises five qualitative forms of inquiry. Thematic analysis was used to code transcripts for common themes in relation to conditions associated with the acceptability of sharing digital footprint data for longitudinal research. RESULTS: We identified six themes: participant understanding; sensitivity of location data; concerns for third parties; clarity on data granularity; mechanisms of data sharing and consent; and trustworthiness of the organisation. For cohort members to consider the sharing of digital footprint data acceptable, they require information about the value, validity and risks; control over sharing elements of the data they consider sensitive; appropriate mechanisms to authorise or object to their records being used; and trust in the organisation. CONCLUSION: Realising the potential for using digital footprint records within longitudinal research will be subject to ensuring that this use of personal data is acceptable; and that rigorously controlled population data science benefiting the public good is distinguishable from the misuse and lack of personal control of similar data within other settings. Participant co-development informs the ethical-governance framework for these novel linkages in a manner which is acceptable and does not undermine the role of the trusted data custodian

Implications of the Top Quark Mass Measurement for the CKM Parameters, xsx_s and CP Asymmetries

Motivated by the recent determination of the top quark mass by the CDF collaboration, \mt =174 \pm 10 ^{+13}_{-12} GeV, we review and update the constraints on the parameters of the quark flavour mixing matrix $V_{CKM}$ in the standard model. In performing our fits, we use inputs from the measurements of the following quantities: (i) \abseps, the CP-violating parameter in $K$ decays, (ii) \delmd, the mass difference due to the \bdbdbar\ mixing, (iii) the matrix elements \absvcb and \absvub, and (iv) $B$-hadron lifetimes. We find that the allowed region of the unitarity triangle is very large, mostly due to theoretical uncertainties. (This emphasizes the importance of measurements of CP-violating rate asymmetries in the $B$ system.) Nevertheless, the present data do somewhat restrict the allowed values of the coupling constant product $f_{B_d}\sqrt{\hat{B}_{B_d}}$ and the renormalization-scale invariant bag constant $\hat{B}_K$. With the updated CKM matrix we present the currently-allowed range of the ratio $\vert V_{td}/V_{ts} \vert$, as well as the standard model predictions for the \bsbsbar\ mixing parameter \xs and the quantities $\sin 2\alpha$, $\sin 2\beta$ and $\sin^2\gamma$, which characterize the CP-asymmetries in $B$-decays. The ALEPH collaboration has recently reported a significant improvement on the lower limit on the \bs-\bsb mass difference, $\Delta M_s/\Delta M_d > 11.3$ (95\% C.L.). This has interesting consequences for the CKM parameters which are also worked out. NOTE: this is a revised and updated version of our previous paper.Comment: LaTeX, 27 pages, 16 uuencoded figures (enclosed), CERN-TH.7398/94, UdeM-GPP-TH-94-0

Numerical Portrait of a Relativistic BCS Gapped Superfluid

We present results of numerical simulations of the 3+1 dimensional Nambu - Jona-Lasinio (NJL) model with a non-zero baryon density enforced via the introduction of a chemical potential mu not equal to 0. The triviality of the model with a number of dimensions d>=4 is dealt with by fitting low energy constants, calculated analytically in the large number of colors (Hartree) limit, to phenomenological values. Non-perturbative measurements of local order parameters for superfluidity and their related susceptibilities show that, in contrast to the 2+1 dimensional model, the ground-state at high chemical potential and low temperature is that of a traditional BCS superfluid. This conclusion is supported by the direct observation of a gap in the dispersion relation for 0.5<=(mu a)<=0.85, which at (mu a)=0.8 is found to be roughly 15% the size of the vacuum fermion mass. We also present results of an initial investigation of the stability of the BCS phase against thermal fluctuations. Finally, we discuss the effect of splitting the Fermi surfaces of the pairing partners by the introduction of a non-zero isospin chemical potential.Comment: 41 pages, 19 figures, uses axodraw.sty, v2: minor typographical correction

ππ\pi\pi scattering in the ρ\rho-meson channel at finite temperature

We study $\pi\pi$ scattering in the I=1, $J^P=1^-$ channel at finite temperature in the framework of the extended Nambu-Jona-Lasinio model that explicitly includes vector and axial-vector degrees of freedom in addition to the usual scalar and pseudoscalar sector. The S-matrix in the coupled channels $q\bar q$ and $\pi \pi$ is constructed via $\rho$-exchange in the $s$-channel. The self-energy of the $\rho$-meson contains both quark and pion loop contributions. The analytic structure of the S-matrix for $T\geq 0$ is investigated and the motion of the $\rho$-pole as a function of coupling constant and temperature is followed in the complex $\sqrt{s}$-plane. For numerical calculations, parameters are chosen in order that $m_\pi$, $f_\pi$ and the experimental $\pi\pi$ phase shifts $\delta_1^1$ at zero temperature are reproduced, and then the behavior of the $\rho$-pole as well as the $\pi\pi$ cross section is investigated as a function of the temperature. We find that the position of the $\rho$ mass stays practically constant for $0\leq T\leq 130$ MeV, and then moves down in energy by about 200 MeV for 130 MeV$\leq T\leq 230$ MeV.Comment: 25 pages, 12 figures, to appear in Nucl. Phys.