On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can improve her utility by more than some fixed factor $\alpha$ through unilateral strategy changes. There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits the demand of each player on a specific resource) such that $\alpha$-approximate pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for $\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold $\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$. For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum

IR MPD CDF<SUB>3</SUB> in two-frequency IR fields

The effectiveness of various sets of laser frequencies was analyzed for two-frequency MPD of CDF3 molecule at the different pressures of buffer gas. It was shown that MPD yield increased compared to either single-frequency or two adjacent frequencies irradiation

A simple technique for the alignment of a ring resonator

A simple technique for the alignment of a ring resonator is presented. The positional and the directional alignments are obtained by the movements of independent mirrors. The effects of alignment inaccuracies on the performance of a ring resonator are discussed

Study of thermally induced active birefringence in Nd:glass laser rods

A study of active birefringence arising due to the thermal stresses in Nd:glass laser rods under different experimental conditions of pumping is reported. The extent of birefringence was measured in terms of depolarization of a pulsed probe beam from a Q-switched Nd:YAG (yttrium aluminum garnet) laser. The maximum depolarization for a 38-mm-diam rod pumped by 12 xenon flash lamps in a circular diffuse reflector configuration was determined to be 2.3%. This value for the depolarization as well as its radial profiles agree well with those determined from a cylindrically symmetric gain profile. In cases of deviation from the cylindrically symmetric pumping, the observed birefringence was found to be more for a clover leaf reflector as compared to that for a circular diffused reflector

Fundamental Limits of the Dispersion of the Two-Photon Absorption Cross-Section

Javier Perez Moreno and Mark G. Kuzyk, J. Chem. Phys. 123, 194101 (2005). (13 pages) We rigorously apply the sum rules to the sum-over-states expression to calculate the fundamental limits of the dispersion of the two-photon absorption cross-section. A comparison of the theory with the data suggests that the truncated sum rules in the three-level model give a reasonable fundamental limit. Our ansatz that the two photon absorption cross-section near the limit must have only three dominant statesis is supported by a rigorous analytical calculation that the resonant term gets smaller as more states are added. We also find that the contributions of the non-explicitly resonant terms can not be neglected when analyzing real molecules with many excited states, even near resonance. However, puzzling as it may be, extrapolating an off-resonant result to resonance using only the resonant term of the three-level model is shown to be consistent with the exact result. In addition, the off-resonant approximation is shown to scale logarithmically when compared with the full three-level model. This scaling can be used to simplify the analysis of measurements. We find that existing molecules are still far from the fundamental limit; so, there is room for improvement. But, reaching the fundamental limit would require precise control of the energy-level spacing, independently of the transition dipole moments -- a task that does not appear possible using today's synthetic approaches. So, we present alternative methods that can still lead to substantial improvements which only require the control of the transition moment to the first excited state. While it is best to normalize measured two photon absorption cross-sections to the fundamental limits when comparing molecules, we show that simply dividing by the square of the number of electrons per molecule yields a good metric for comparison

A plasma shutter to generate a synchronized subnanosecond pulse for optical probing of laser-produced plasmas

A simple and reliable technique to temporally shorten a multinanosecond Nd:glass laser pulse to less than nanosecond duration at the second harmonic wavelength is described in this article. Using this technique a short probe pulse synchronized with the main laser was generated for optical probing of laser-produced plasmas. Experiments reported were conducted with a Nd:glass laser of wavelength 1.06 μm and of 20 ns duration to yield a temporally shortened pulse of duration less than a nanosecond at a wavelength of 0.53 μm. This technique would be particularly useful and give better results for shorter wavelength lasers (UV and VUV) for which the conventional techniques of pulse slicing are sophisticated as well as add to the expense and complexity of the laser system

Performance characteristics of a Nd: glass laser amplifier from fluorescence emission studies

The dependence of cavity transfer efficiency of a Nd: glass laser amplifier on flashlamp current density is obtained from the analysis of amplified fluorescence. The cavity transfer efficiency decreases as the current density through the flashlamps is increased. The use of the fluorescence method in optimizing the flashlamp pulse duration for achieving maximum gain in the amplifier is illustrated

Current-limited capacitor charging power supply for spark-gap-driven high repetition rate laser pulser

A short-circuit protected capacitor charging scheme for a spark-gap driven high repetition rate laser pulser is described. The possibility of using this scheme with a thyratron driven laser pulser is also discussed