2-Player Nash and Nonsymmetric Bargaining Games: Algorithms and Structural Properties

The solution to a Nash or a nonsymmetric bargaining game is obtained by maximizing a concave function over a convex set, i.e., it is the solution to a convex program. We show that each 2-player game whose convex program has linear constraints, admits a rational solution and such a solution can be found in polynomial time using only an LP solver. If in addition, the game is succinct, i.e., the coefficients in its convex program are ``small'', then its solution can be found in strongly polynomial time. We also give a non-succinct linear game whose solution can be found in strongly polynomial time

Average features of the muon component of EAS or = 10(17) eV

Three 10 sq m liquid scintillators were situated at approximately 0 m, 150 m and 250 m from the center of the Haverah Park array. The detectors were shielded by lead/barytes giving muon detection thresholds of 317 MeV, 431 MeV and 488 MeV respectively. During part of the operational period the 431 MeV threshold was lowered to 313 MeV for comparison purposes. For risetime measurement fast phototubes were used and the 10% to 70% amplitude time interval was parameterized by T sub 70. A muon lateral density distribution of the form rho mu (R theta) = krho(500)0.94 1/R(1 + R/490)-eta has been fitted to the data for 120 m R 600 m and 0.27 (500) 2.55. The shower size parameter (500) is the water Cerenkov response at 500 m from the core of the extensive air showers (EAS) and is relatable to the primary energy. The results show general consistency

Muon fluctuation studies of EAS 10(17) eV

Fluctuation studies need to compare a parameter which is sensitive to longitudinal fluctuations against a parameter which is insensitive. Cascade calculations indicate that the shower size parameter at Haverah Park, rho (500), and the muon density are insensitive while parameters that significantly reflect the longitudinal development of a particular extensive air shower (EAS) include the muon/water Cerenkov response ratio and the muon arrival time dispersion. This paper presents conclusions based on muon fluctuation studies of EAS measured between 1976 and 1981 at Haverah Park

The muon content of EAS as a function of primary energy

The muon content of extensive air showers (EAS) was measured over the wide primary energy range 10 to the 16th power to 10 to the 20th power eV. It is reported that the relative muon content of EAS decreases smoothly over the energy range 10 to the 17th power to 10 to the 19th power eV and concluded that the primary cosmic ray flux has a constant mass composition over this range. It is also reported that an apparent significant change in the power index occurs below 10 to the 17th power eV rho sub c (250 m) sup 0.78. Such a change indicates a significant change in primary mass composition in this range. The earlier conclusions concerning EAS of energy 10 to the 17th power eV are confirmed. Analysis of data in the 10 to the 16th power - 10 to the 17th power eV range revealed a previously overlooked selection bias in the data set. The full analysis of the complete data set in the energy range 10 to the 16th power - 10 to the 17th power ev with the selection bias eliminated is presented

Run-and-tumble particles with hydrodynamics: sedimentation, trapping and upstream swimming

We simulate by lattice Boltzmann the nonequilibrium steady states of run-and-tumble particles (inspired by a minimal model of bacteria), interacting by far-field hydrodynamics, subject to confinement. Under gravity, hydrodynamic interactions barely perturb the steady state found without them, but for particles in a harmonic trap such a state is quite changed if the run length is larger than the confinement length: a self-assembled pump is formed. Particles likewise confined in a narrow channel show a generic upstream flux in Poiseuille flow: chiral swimming is not required

Social work education, training and standards in the Asia-Pacific region

This article discusses the joint project between the International Association of Schools of Social Work (IASSW) and the International Federation of Social Workers (IFSW) to establish guidelines for the training and standard setting that elucidates what social work represents on a global level. While it is impossible to address all the issues that might be significant in such a large scope, attention is given to the challenges establishing global standards might encounter in a region as diverse as the Asia-Pacific

Near-Optimal Computation of Runs over General Alphabet via Non-Crossing LCE Queries

Longest common extension queries (LCE queries) and runs are ubiquitous in algorithmic stringology. Linear-time algorithms computing runs and preprocessing for constant-time LCE queries have been known for over a decade. However, these algorithms assume a linearly-sortable integer alphabet. A recent breakthrough paper by Bannai et.\ al.\ (SODA 2015) showed a link between the two notions: all the runs in a string can be computed via a linear number of LCE queries. The first to consider these problems over a general ordered alphabet was Kosolobov (\emph{Inf.\ Process.\ Lett.}, 2016), who presented an $O(n (\log n)^{2/3})$-time algorithm for answering $O(n)$ LCE queries. This result was improved by Gawrychowski et.\ al.\ (accepted to CPM 2016) to $O(n \log \log n)$ time. In this work we note a special \emph{non-crossing} property of LCE queries asked in the runs computation. We show that any $n$ such non-crossing queries can be answered on-line in $O(n \alpha(n))$ time, which yields an $O(n \alpha(n))$-time algorithm for computing runs

Finite element analysis applied to redesign of submerged entry nozzles for steelmaking

The production of steel by continuous casting is facilitated by the use of refractory hollow-ware components. A critical component in this process is the submerged entry nozzle (SEN). The normal operating conditions of the SEN are arduous, involving large temperature gradients and exposure to mechanical forces arising from the flow of molten steel; experimental development of the components is challenging in so hazardous an environment. The effects of the thermal stress conditions in relation to a well-tried design were therefore simulated using a finite element analysis approach. It was concluded from analyses that failures of the type being experienced are caused by the large temperature gradient within the nozzle. The analyses pointed towards a supported shoulder area of the nozzle being most vulnerable to failure and practical in-service experience confirmed this. As a direct consequence of the investigation, design modifications, incorporating changes to both the internal geometry and to the nature of the intermediate support material, were implemented, thereby substantially reducing the stresses within the Al2O3/graphite ceramic liner. Industrial trials of this modified design established that the component reliability would be significantly improved and the design has now been implemented in series production

Multiplayer Cost Games with Simple Nash Equilibria

Multiplayer games with selfish agents naturally occur in the design of distributed and embedded systems. As the goals of selfish agents are usually neither equivalent nor antagonistic to each other, such games are non zero-sum games. We study such games and show that a large class of these games, including games where the individual objectives are mean- or discounted-payoff, or quantitative reachability, and show that they do not only have a solution, but a simple solution. We establish the existence of Nash equilibria that are composed of k memoryless strategies for each agent in a setting with k agents, one main and k-1 minor strategies. The main strategy describes what happens when all agents comply, whereas the minor strategies ensure that all other agents immediately start to co-operate against the agent who first deviates from the plan. This simplicity is important, as rational agents are an idealisation. Realistically, agents have to decide on their moves with very limited resources, and complicated strategies that require exponential--or even non-elementary--implementations cannot realistically be implemented. The existence of simple strategies that we prove in this paper therefore holds a promise of implementability.Comment: 23 page