Query Complexity of Approximate Equilibria in Anonymous Games

We study the computation of equilibria of anonymous games, via algorithms that may proceed via a sequence of adaptive queries to the game's payoff function, assumed to be unknown initially. The general topic we consider is \emph{query complexity}, that is, how many queries are necessary or sufficient to compute an exact or approximate Nash equilibrium. We show that exact equilibria cannot be found via query-efficient algorithms. We also give an example of a 2-strategy, 3-player anonymous game that does not have any exact Nash equilibrium in rational numbers. However, more positive query-complexity bounds are attainable if either further symmetries of the utility functions are assumed or we focus on approximate equilibria. We investigate four sub-classes of anonymous games previously considered by \cite{bfh09, dp14}. Our main result is a new randomized query-efficient algorithm that finds a $O(n^{-1/4})$-approximate Nash equilibrium querying $\tilde{O}(n^{3/2})$ payoffs and runs in time $\tilde{O}(n^{3/2})$. This improves on the running time of pre-existing algorithms for approximate equilibria of anonymous games, and is the first one to obtain an inverse polynomial approximation in poly-time. We also show how this can be utilized as an efficient polynomial-time approximation scheme (PTAS). Furthermore, we prove that $\Omega(n \log{n})$ payoffs must be queried in order to find any $\epsilon$-well-supported Nash equilibrium, even by randomized algorithms

Measurement of the solenoid magnetic field

We describe the machine used to map the solenoid field and the data sets that were collected. The bulk of the note describes the analysis of this data. A series of small corrections are made; some taken from surveys and some derived from the data itself. Two fitting methods are defined and applied to all data sets. The final result is that the field map at normal operating current can be fitted to a function that obeys Maxwell with an r.m.s. residual of less than 5 Gauss. Systematic errors on the measurement of track sagitta due to the field uncertainty are estimated to be in the range 2.3E-4 to 12E-4, depending on the track rapidity. Finally, the representation of the map in Athena is briefly described

Some properties of the newly observed X(1835) state at BES

Recently the BES collaboration has announced observation of a resonant state in the $\pi^+\pi^- \eta'$ spectrum in $J/\psi \to \gamma \pi^+\pi^-\eta'$ decay. Fitting the data with a $0^{-+}$ state, the mass is determined to be 1833.7 MeV with $7.7\sigma$ statistic significance. This state is consistent with the one extracted from previously reported $p \bar p$ threshold enhancement data in $J/\psi \to \gamma p \bar p$. We study the properties of this state using QCD anomaly and QCD sum rules assuming X(1835) to be a pseudoscalar and show that it is consistent with data. We find that this state has a sizeable matrix element $$ leading to branching ratios of $(2.61\sim 7.37)\times 10^{-3}$ and $(2.21\sim 10.61)\times 10^{-2}$ for $J/\psi \to \gamma G_p$ and for $G_p \to \pi^+\pi^- \eta'$, respectively. Combining the calculated branching ratio of $J/\psi \to \gamma G_p$ and data on threshold enhancement in $J/\psi \to \gamma p \bar p$, we determine the coupling for $G_p- p-\bar p$ interaction. We finally study branching ratios of other $J/\psi \to \gamma + {three mesons}$ decay modes. We find that $J/\psi \to \gamma G_p \to \gamma (\pi^+\pi^- \eta, K K \pi^0)$ can provide useful tests for the mechanism proposed.Comment: 13 pages, 3 figures. The final version to appear at EPJ

Recommendations of protective measures for orthopedic surgeons during COVID-19 pandemic

PURPOSE: It was the primary purpose of the present systematic review to identify the optimal protection measures during COVID-19 pandemic and provide guidance of protective measures for orthopedic surgeons. The secondary purpose was to report the protection experience of an orthopedic trauma center in Wuhan, China during the pandemic. METHODS: A systematic search of the PubMed, Cochrane, Web of Science, Google Scholar was performed for studies about COVID-19, fracture, trauma, orthopedic, healthcare workers, protection, telemedicine. The appropriate protective measures for orthopedic surgeons and patients were reviewed (on-site first aid, emergency room, operating room, isolation wards, general ward, etc.) during the entire diagnosis and treatment process of traumatic patients. RESULTS: Eighteen studies were included, and most studies (13/18) emphasized that orthopedic surgeons should pay attention to prevent cross-infection. Only four studies have reported in detail how orthopedic surgeons should be protected during surgery in the operating room. No detailed studies on multidisciplinary cooperation, strict protection, protection training, indications of emergency surgery, first aid on-site and protection in orthopedic wards were found. CONCLUSION: Strict protection at every step in the patient pathway is important to reduce the risk of cross-infection. Lessons learnt from our experience provide some recommendations of protective measures during the entire diagnosis and treatment process of traumatic patients and help others to manage orthopedic patients with COVID-19, to reduce the risk of cross-infection between patients and to protect healthcare workers during work. LEVEL OF EVIDENCE: IV

Perturbative QCD at non-zero chemical potential: Comparison with the large-Nf limit and apparent convergence

The perturbative three-loop result for the thermodynamic potential of QCD at finite temperature and chemical potential as obtained in the framework of dimensional reduction is compared with the exact result in the limit of large flavor number. The apparent convergence of the former as well as possibilities for optimization are investigated. Corresponding optimized results for full QCD are given for the case of two massless quark flavors.Comment: REVTEX4, 4 pages, 3 color figures. v2: fig. 3 now includes also lattice data for two-flavor QCD at nonzero chemical potentia

Measurement of the ATLAS solenoid magnetic field

ATLAS is a general purpose detector designed to explore a wide range of physics at the Large Hadron Collider. At the centre of ATLAS is a tracking detector in a 2 T solenoidal magnetic field. This paper describes the machine built to map the field, the data analysis methods, the final results, and their estimated uncertainties. The remotely controlled mapping machine used pneumatic motors with feedback from optical encoders to scan an array of Hall probes over the field volume and log data at more than 20 000 points in a few hours. The data were analysed, making full use of the physical constraints on the field and of our knowledge of the solenoid coil geometry. After a series of small corrections derived from the data itself, the resulting maps were fitted with a function obeying Maxwell's equations. The fit residuals had an r.m.s. less than 0.5 mT and the systematic error on the measurement of track sagitta due to the field uncertainty was estimated to be in the range 0.02 % to 0.12 % depending on the track rapidity

A Hybrid Global Minimization Scheme for Accurate Source Localization in Sensor Networks

We consider the localization problem of multiple wideband sources in a multi-path environment by coherently taking into account the attenuation characteristics and the time delays in the reception of the signal. Our proposed method leaves the space for unavailability of an accurate signal attenuation model in the environment by considering the model as an unknown function with reasonable prior assumptions about its functional space. Such approach is capable of enhancing the localization performance compared to only utilizing the signal attenuation information or the time delays. In this paper, the localization problem is modeled as a cost function in terms of the source locations, attenuation model parameters and the multi-path parameters. To globally perform the minimization, we propose a hybrid algorithm combining the differential evolution algorithm with the Levenberg-Marquardt algorithm. Besides the proposed combination of optimization schemes, supporting the technical details such as closed forms of cost function sensitivity matrices are provided. Finally, the validity of the proposed method is examined in several localization scenarios, taking into account the noise in the environment, the multi-path phenomenon and considering the sensors not being synchronized

Time to look for evidence : Results-based approach to biodiversity conservation on farmland in Europe

Increased use of annual payments to land managers for ecological outcomes indicates a growing interest in exploring the potential of this approach. In this viewpoint, we drew on the experiences of all schemes paying for biodiversity outcomes/results on agricultural land operating in the EU and EFTA countries with the aim of reviewing the decisive elements of the schemes' design and implementation as well as the challenges and opportunities of adopting a results-based approach. We analysed the characteristics of results-based schemes using evidence from peer-reviewed literature, technical reports, scheme practitioners and experts in agri-environment-climate policy. We developed a typology of the schemes and explored critical issues influencing the feasibility and performance of results-based schemes. The evidence to date shows that there are at least 11 advantages to the results-based approach not found in management-based schemes with similar objectives, dealing with environmental efficiency, farmers' participation and development of local biodiversity-based projects. Although results-based approaches have specific challenges at every stage of design and implementation, for many of these the existing schemes provide potential solutions. There is also some apprehension about trying a results-based approach in Mediterranean, central and eastern EU Member States. We conclude that there is clear potential to expand the approach in the European Union for the Rural Development programming period for 2021-2028. Nevertheless, evidence is needed about the approach's efficiency in delivering conservation outcomes in the long term, its additionality, impact on the knowledge and attitudes of land managers and society at large, development of ways of rewarding the achievement of actual results, as well as its potential for stimulating innovative grassroots solutions.Peer reviewe

Caspase-2 is upregulated after sciatic nerve transection and its inhibition protects dorsal root ganglion neurons from Apoptosis after serum withdrawal

Sciatic nerve (SN) transection-induced apoptosis of dorsal root ganglion neurons (DRGN) is one factor determining the efficacy of peripheral axonal regeneration and the return of sensation. Here, we tested the hypothesis that caspase-2(CASP2) orchestrates apoptosis of axotomised DRGN both in vivo and in vitro by disrupting the local neurotrophic supply to DRGN. We observed significantly elevated levels of cleaved CASP2 (C-CASP2), compared to cleaved caspase-3 (C-CASP3), within TUNEL+DRGN and DRG glia (satellite and Schwann cells) after SN transection. A serum withdrawal cell culture model, which induced 40% apoptotic death in DRGN and 60% in glia, was used to model DRGN loss after neurotrophic factor withdrawal. Elevated C-CASP2 and TUNEL were observed in both DRGN and DRG glia, with C-CASP2 localisation shifting from the cytosol to the nucleus, a required step for induction of direct CASP2-mediated apoptosis. Furthermore, siRNAmediated downregulation of CASP2 protected 50% of DRGN from apoptosis after serum withdrawal, while downregulation of CASP3 had no effect on DRGN or DRG glia survival. We conclude that CASP2 orchestrates the death of SN-axotomised DRGN directly and also indirectly through loss of DRG glia and their local neurotrophic factor support. Accordingly, inhibiting CASP2 expression is a potential therapy for improving both the SN regeneration response and peripheral sensory recovery

A road to reality with topological superconductors

Topological states of matter are a source of low-energy quasiparticles, bound to a defect or propagating along the surface. In a superconductor these are Majorana fermions, described by a real rather than a complex wave function. The absence of complex phase factors promises protection against decoherence in quantum computations based on topological superconductivity. This is a tutorial style introduction written for a Nature Physics focus issue on topological matter.Comment: pre-copy-editing, author-produced version of the published paper: 4 pages, 2 figure