Finding optimal Stackelberg production strategies: How to produce in times of war?

Inspired by a military context, we study a Stackelberg production game where a country's government, the leader, wants to maximize the production of military assets. The leader does so by allocating his resources among a set of production facilities. His opponent, the follower, observes this allocation and tries to destroy the associated production as much as possible by allocating his destructive resources, for example bombs, among these facilities. In this paper, we identify a follower's optimal strategy. For the leader, we show that an optimal production strategy can be found in the class of so-called seried-balanced strategies. We present a linear time algorithm that finds an optimal strategy in this class

Validity of adiabaticity in Cavity QED

This paper deals with the concept of adiabaticity for fully quantum mechanically cavity QED models. The physically interesting cases of Gaussian and standing wave shapes of the cavity mode are considered. An analytical approximate measure for adiabaticity is given and compared with numerical wave packet simulations. Good agreement is obtained where the approximations are expected to be valid. Usually for cavity QED systems, the large atom-field detuning case is considered as the adiabatic limit. We, however, show that adiabaticity is also valid, for the Gaussian mode shape, in the opposite limit. Effective semiclassical time dependent models, which do not take into account the shape of the wave packet, are derived. Corrections to such an effective theory, which are purely quantum mechanical, are discussed. It is shown that many of the results presented can be applied to time dependent two-level systems.Comment: 10 pages, 9 figure

Core Allocations for Cooperation Problems in Vaccination

Vaccination is a very effective measure to fight an outbreak of an infectious disease, but it often suffers from delayed deliveries and limited stockpiles. To use these limited doses of vaccine effectively, health agencies can decide to cooperate and share their doses. In this study, we analyze this type of cooperation. Typically cooperation leads to an increased total return, but cooperation is only plausible when this total return can be distributed in a stable way. This makes cooperation a delicate matter. Using cooperative game theory, we derive theoretical sufficient conditions under which cooperation is plausible (i.e., the core is non-empty) and we show that the doses of vaccine can be traded for a market price in those cases. We perform numerical analyses to generalize these findings and we derive analytical expressions for market prices that can be used in general for distributing the total return. Our results demonstrate that cooperation is most likely to be plausible in case of severe shortages and in case of sufficient supply, with possible mismatches between supply and demand. In those cases, trading doses of vaccine for a market price often results in a core allocation of the total return. We confirm these findings with a case study on the redistribution of influenza vaccines

Strong-field approximation for intense-laser atom processes: the choice of gauge

The strong-field approximation can be and has been applied in both length gauge and velocity gauge with quantitatively conflicting answers. For ionization of negative ions with a ground state of odd parity, the predictions of the two gauges differ qualitatively: in the envelope of the angular-resolved energy spectrum, dips in one gauge correspond to humps in the other. We show that the length-gauge SFA matches the exact numerical solution of the time-dependent Schr\"odinger equation.Comment: 5 pages, 3 figures, revtex

Resource location games

In this paper, we introduce and analyze resource location games. We show core nonemptiness by providing a set of intuitive core allocations, called Resource-Profit allocations. In addition, we present a sufficient condition for which the core and the set of Resource- Profit allocations coincide. Finally, we provide an example showing that when the sufficient condition is not satisfied, the coincidence is not guaranteed

Relativistic and Radiative Corrections to the Mollow Spectrum

The incoherent, inelastic part of the resonance fluorescence spectrum of a laser-driven atom is known as the Mollow spectrum [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. Starting from this level of description, we discuss theoretical foundations of high-precision spectroscopy using the resonance fluorescence light of strongly laser-driven atoms. Specifically, we evaluate the leading relativistic and radiative corrections to the Mollow spectrum, up to the relative orders of (Z alpha)^2 and alpha(Z alpha)^2, respectively, and Bloch-Siegert shifts as well as stimulated radiative corrections involving off-resonant virtual states. Complete results are provided for the hydrogen 1S-2P_{1/2} and 1S-2P_{3/2} transitions; these include all relevant correction terms up to the specified order of approximation and could directly be compared to experimental data. As an application, the outcome of such experiments would allow for a sensitive test of the validity of the dressed-state basis as the natural description of the combined atom-laser system.Comment: 20 pages, 1 figure; RevTe

Self-Energy Correction to the Two-Photon Decay Width in Hydrogenlike Atoms

We investigate the gauge invariance of the leading logarithmic radiative correction to the two-photon decay width in hydrogenlike atoms. It is shown that an effective treatment of the correction using a Lamb-shift "potential" leads to equivalent results in both the length as well as the velocity gauges provided all relevant correction terms are taken into account. Specifically, the relevant radiative corrections are related to the energies that enter into the propagator denominators, to the Hamiltonian, to the wave functions, and to the energy conservation condition that holds between the two photons; the form of all of these effects is different in the two gauges, but the final result is shown to be gauge invariant, as it should be. Although the actual calculation only involves integrations over nonrelativistic hydrogenic Green functions, the derivation of the leading logarithmic correction can be regarded as slightly more complex than that of other typical logarithmic terms. The dominant radiative correction to the 2S two-photon decay width is found to be -2.020536 (alpha/pi) (Zalpha)^2 ln[(Zalpha)^-2] in units of the leading nonrelativistic expression. This result is in agreement with a length-gauge calculation [S. G. Karshenboim and V. G. Ivanov, e-print physics/9702027], where the coefficient was given as -2.025(1).Comment: 9 pages, RevTe

Calcific myofibrosis due to pentazocine abuse: a case report

<p>Abstract</p> <p>Introduction</p> <p>Pentazocine, a synthetic narcotic analgesic, is commonly used for the relief of moderate to severe pain secondary to various conditions. It is usually well tolerated; however, adverse effects are not uncommon, especially when higher doses are used and when it is used in a dependent fashion. There have been reports of various complications associated with its use, including skin fibrosis, skin ulceration, abnormal skin pigmentation and symmetrical myopathy with fibrous myopathy. Fibrosis has usually been reported in the muscles at the site of injection of the drug. Being opioid in nature, it has a high abuse potential.</p> <p>Case presentation</p> <p>Here we report a case of pentazocine-induced calcific myofibrosis in a 42-year-old man involving muscles which were not injected with pentazocine.</p> <p>Conclusion</p> <p>This case highlights the care that needs to be taken when prescribing opioid analgesics, such as pentazocine, as routine painkillers. Patients who have history of substance abuse are more likely to abuse other agents, including prescription drugs. Rare consequences such as calcific myofibrosis are devastating and can cause significant lifelong disability.</p