New algorithms for approximate Nash equilibria in bimatrix games

We consider the problem of computing additively approximate Nash equilibria in non-cooperative two-player games. We provide a new polynomial time algorithm that achieves an approximation guarantee of 0.36392. Our work improves the previously best known (0.38197¿+¿e)-approximation algorithm of Daskalakis, Mehta and Papadimitriou [6]. First, we provide a simpler algorithm, which also achieves 0.38197. This algorithm is then tuned, improving the approximation error to 0.36392. Our method is relatively fast, as it requires solving only one linear program and it is based on using the solution of an auxiliary zero-sum game as a starting point. The first author was supported by NWO. The second and third author were supported by the EU Marie Curie Research Training Network, contract numbers MRTN-CT-2003-504438-ADONET and MRTN-CT-2004-504438-ADONET respectively

SUBARU and e-Merlin observations of NGC3718. Diaries of an SMBH recoil?

NGC3718 is a LINER $L1.9$ galaxy, lying at a distance of about $\sim 17.4$ Mpc away from earth and its similarities with NGC5128 often award it the name "northern Centaurus A". We use high angular resolution ($\sim100$ mas) e-Merlin radio and SUBARU NIR ($\sim170$ mas) data, to take a detailed view of the processes taking place in its central region. In order to preserve some objectivity in our interpretation, we combine our results with literature values and findings from previous studies. Our NIR maps suggest, on one hand, that towards the stellar bulge there are no large scale absorption phenomena caused by the apparent dust lane and, on the other, that there is a significant (local) contribution from hot ($\sim1000$ K) dust to the nuclear NIR emission. The position where this takes place appears to be closer to the offset compact radio emission from our e-Merlin $6$ cm map, lying offset by $\sim4.25$ pc from the center of the underlying stellar bulge. The shape of the radio map suggests the presence of one (or possibly two, forming an X-shape) bipolar structure(s) $\sim1$ ($\sim0.6$) arcsec across, which combined with the balance between the gas and the stellar velocity dispersions and the presence of hard X-ray emission, point towards effects expected by AGN feedback. We also argue that NGC3718 has a "core" in its surface brightness profile, despite the fact that it is a gas-rich galaxy and we discuss its mixed photometric and spectroscopic characteristics. The latter combined with the observed spatial and radio offsets, the relative redshift between the broad and the narrow $H{\mathrm{\alpha}}$ line, the limited star formation activity and AGN feedback, strongly imply the existence of an SMBH recoil. Finally, we discuss a possible interpretation, that could naturally incorporate all these findings into one physically consistent picture.Comment: 18 pages, 18 figures, 3 tables, accepted for publications in A&

High resolution observations of Cen A: Yellow and red supergiants in a region of jet-induced star formation?

We present the analysis of near infrared (NIR), adaptive optics (AO) Subaru and archived HST imaging data of a region near the northern middle lobe (NML) of the Centaurus A (Cen A) jet, at a distance of $\sim15$ kpc north-east (NE) from the center of NGC5128. Low-pass filtering of the NIR images reveals strong -- $>3\sigma$ above the background mean -- signal at the expected position of the brightest star in the equivalent HST field. Statistical analysis of the NIR background noise suggests that the probability to observe $>3\sigma$ signal at the same position, in three independent measurements due to stochastic background fluctuations alone is negligible ($\leq10^{-7}\%$) and, therefore, that this signal should reflect the detection of the NIR counterparts of the brightest HST star. An extensive photometric analysis of this star yields $V-I$, visual-NIR, and NIR colors expected from a yellow supergiant (YSG) with an estimated age $\sim10^{+4}_{-3}$ Myr. Furthermore, the second and third brighter HST stars are, likely, also supergiants in Cen A, with estimated ages $\sim16^{+6}_{-3}$ Myr and $\sim25^{+15}_{-9}$ Myr, respectively. The ages of these three supergiants are in good agreement with the ages of the young massive stars that were previously found in the vicinity and are thought to have formed during the later phases of the jet-HI cloud interaction that appears to drive the star formation (SF) in the region for the past $\sim100$ Myr.Comment: 11 pages, 6 figures, 2 tables, accepted for publication in Ap

On the learning benefits of resource flexibility

Resource flexibility, arguably among the most celebrated operational concepts, is known to provide firms facing demand uncertainty with such benefits as risk pooling, revenue-maximization optionality, and operational hedging. In this paper, we uncover a heretofore unknown benefit: we establish that resource flexibility facilitates learning the demand when the latter is censored, which could, in turn, enable firms to make better-informed future operational decisions, thereby increasing profitability. Further, we quantify these learning benefits of flexibility and find that they could be of the same order of magnitude as the extensively studied risk-pooling benefits of flexibility. This suggests that flexibility’s learning benefits could be a first-order consideration and that extant theories, which view flexibility only as the ability to act ex post, could be underestimating its true value when learning the demand is desirable, for example, when it enables managers to make better ex ante capacity, assortment, or pricing decisions in future periods

Complexity of Strong Implementability

We consider the question of implementability of a social choice function in a classical setting where the preferences of finitely many selfish individuals with private information have to be aggregated towards a social choice. This is one of the central questions in mechanism design. If the concept of weak implementation is considered, the Revelation Principle states that one can restrict attention to truthful implementations and direct revelation mechanisms, which implies that implementability of a social choice function is easy to check. For the concept of strong implementation, however, the Revelation Principle becomes invalid, and the complexity of deciding whether a given social choice function is strongly implementable has been open so far. In this paper, we show by using methods from polyhedral theory that strong implementability of a social choice function can be decided in polynomial space and that each of the payments needed for strong implementation can always be chosen to be of polynomial encoding length. Moreover, we show that strong implementability of a social choice function involving only a single selfish individual can be decided in polynomial time via linear programming

An engineered E. coli strain for direct in vivo fluorination

This work was funded by the Industrial Biotechnology Innovation Centre (IBioIC) with support from GlaxoSmithKline, and also the EU Horizon 2020 (Sinfonia consortia).Selectively fluorinated compounds are found frequently in pharmaceutical and agrochemical products where currently 25–30 % of optimised compounds emerge from development containing at least one fluorine atom. There are many methods for the site‐specific introduction of fluorine, but all are chemical and they often use environmentally challenging reagents. Biochemical processes for C−F bond formation are attractive, but they are extremely rare. In this work, the fluorinase enzyme, originally identified from the actinomycete bacterium Streptomyces cattleya, is engineered into Escherichia coli in such a manner that the organism is able to produce 5′‐fluorodeoxyadenosine (5′‐FDA) from S‐adenosyl‐l‐methionine (SAM) and fluoride in live E. coli cells. Success required the introduction of a SAM transporter and deletion of the endogenous fluoride efflux capacity in order to generate an E. coli host that has the potential for future engineering of more elaborate fluorometabolites.PostprintPeer reviewe

Measuring the neutron star equation of state with gravitational wave observations

We report the results of a first study that uses numerical simulations to estimate the accuracy with which one can use gravitational wave observations of double neutron star inspiral to measure parameters of the neutron-star equation of state. The simulations use the evolution and initial-data codes of Shibata and Uryu to compute the last several orbits and the merger of neutron stars, with matter described by a parametrized equation of state. Previous work suggested the use of an effective cutoff frequency to place constraints on the equation of state. We find, however, that greater accuracy is obtained by measuring departures from the point-particle limit of the gravitational waveform produced during the late inspiral. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly for smaller values of the neutron star compactness (the ratio of the mass of the neutron star to its radius). We estimate that realistic equations of state will lead to gravitational waveforms that are distinguishable from point particle inspirals at an effective distance (the distance to an optimally oriented and located system that would produce an equivalent waveform amplitude) of 100 Mpc or less. As Lattimer and Prakash observed, neutron-star radius is closely tied to the pressure at density not far above nuclear. Our results suggest that broadband gravitational wave observations at frequencies between 500 and 1000 Hz will constrain this pressure, and we estimate the accuracy with which it can be measured. Related first estimates of radius measurability show that the radius can be determined to an accuracy of ~1 km at 100 Mpc.Comment: 12 pages, 5 figures, to be submitted to Phys. Rev.

Quasi-equilibrium models for triaxially deformed rotating compact stars

Quasi-equilibrium models of rapidly rotating triaxially deformed stars are computed in general relativistic gravity, assuming a conformally flat spatial geometry (Isenberg-Wilson-Mathews formulation) and a polytropic equation of state. Highly deformed solutions are calculated on the initial slice covered by spherical coordinate grids, centered at the source, in all angular directions up to a large truncation radius. Constant rest mass sequences are calculated from nearly axisymmetric to maximally deformed triaxial configurations. Selected parameters are to model (proto-) neutron stars; the compactness is M/R = 0.001, 0.1, 0.14, 0.2 for polytropic index n = 0.3 and M/R = 0.001, 0.1, 0.12, 0.14 for n = 0.5. We confirmed that the triaxial solutions exist for these parameters as in the case of Newtonian polytropes. However, it is also found that the triaxial sequences become shorter for higher compactness, and those may disappear at a certain large compactness for the n = 0.5 case. In the scenario of the contraction of proto-neutron stars being subject to strong viscosity and rapid cooling, it is plausible that, once the viscosity driven secular instability sets in during the contraction, the proto-neutron stars are always maximally deformed triaxial configurations, as long as the compactness and the equation of state parameters allow such triaxial sequences. Detection of gravitational waves from such sources may be used as another probe for the nuclear equation of state.Comment: 13 pages, 5 figure