On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

Liquid Crystal Polarimetry for Metastability Exchange Optical Pumping of 3He

We detail the design and operation of a compact, discharge light polarimeter for metastability exchange optical pumping of 3He gas near 1 torr under a low magnetic field. The nuclear polarization of 3He can be discerned from its electron polarization, measured via the circular polarization of 668 nm discharge light from an RF excitation. This apparatus measures the circular polarization of this very dim discharge light using a nematic liquid crystal wave retarder (LCR) and a high-gain, transimpedance amplified Si photodiode. We outline corrections required in such a measurement, and discuss contributions to its systematic error

The Prevalence of Carbon-13 in Respiratory Carbon Dioxide As an Indicator of the Type of Endogenous Substrate. The change from lipid to carbohydrate during the respiratory rise in potato slices

Isotope discrimination is a common feature of biosynthesis in nature, with the result that different classes of carbon compounds frequently display different 13C/12C ratios. The 13C/12C ratio of lipid in potato tuber tissue is considerably lower than that for starch or protein. We have collected respiratory CO2 from potato discs in successive periods through 24 hr from the time of cutting—an interval in which the respiration rate rises 3–5-fold. The 13C/12C ratio of the evolved CO2 was determined for each period, and compared with the 13C/12C ratios of the major tissue metabolites. In the first hours the carbon isotope ratio of the CO2 matches that of lipid. With time, the ratio approaches that typical of starch or protein. An estimation has been made of the contribution of lipid and carbohydrate to the total respiration at each juncture. In connection with additional observations, it was deduced that the basal, or initial, respiration represents lipid metabolism —- possibly the alpha-oxidation of long chain fatty acids -— while the developed repiration represents conventional tricarboxylic acid cycle oxidation of the products of carbohydrate glycolysis. The true isotopic composition of the respiratory CO2 may be obscured by fractionation attending the refixation of CO2 during respiration, and by CO2 arising from dissolved CO2 and bicarbonate preexisting in the tuber. Means are described for coping with both pitfalls

Stable hydrogen and carbon isotope ratios of extractable hydrocarbons in the Murchison meteorite

A fairly fool-proof method to ensure that the compounds isolated from meteorites are truly part of the meteorites and not an artifact introduced by exposure to the terrestrial environment, storage, or handling is presented. The stable carbon and hydrogen isotope ratios in several of the chemical compounds extracted from the Murchison meteorite were measured. The results obtained by studying the amino acids in this meteorite gave very unusual hydrogen and carbon isotope ratios. The technique was extended to the different classes of hydrocarbons and the hydrocarbons were isolated using a variety of separation techniques. The results and methods used in this investigation are described in this two page paper

Thermoelectric Amplification of Phonons in Graphene

Amplification of acoustic phonons due to an external temperature gredient ($\nabla T$) in Graphene was studied theoretically. The threshold temperature gradient $(\nabla T)_0^{g}$ at which absorption switches over to amplification in Graphene was evaluated at various frequencies $\omega_q$ and temperatures $T$. For $T = 77K$ and frequency $\omega_q = 12THz$, $(\nabla T)_0^{g} = 0.37Km^{-1}$. The calculation was done in the regime at $ql >> 1$. The dependence of the normalized ($\Gamma/\Gamma_0$) on the frequency $\omega_q$ and the temperature gradient $(\nabla T/T)$ are evaluated numerically and presented graphically. The calculated $(\nabla T)_0^{g}$ for Graphene is lower than that obtained for homogeneous semiconductors ($n-InSb$) $(\nabla T)_0^{hom} \approx 10^3Kcm^{-1}$, Superlattices $(\nabla T)_0^{SL} = 384Kcm^{-1}$, Cylindrical Quantum Wire $(\nabla T)_0^{cqw} \approx 10^2Kcm^{-1}$. This makes Graphene a much better material for thermoelectric phonon amplifier.Comment: 12 Pages, 6 figure

Abstract Tensor Systems as Monoidal Categories

The primary contribution of this paper is to give a formal, categorical treatment to Penrose's abstract tensor notation, in the context of traced symmetric monoidal categories. To do so, we introduce a typed, sum-free version of an abstract tensor system and demonstrate the construction of its associated category. We then show that the associated category of the free abstract tensor system is in fact the free traced symmetric monoidal category on a monoidal signature. A notable consequence of this result is a simple proof for the soundness and completeness of the diagrammatic language for traced symmetric monoidal categories.Comment: Dedicated to Joachim Lambek on the occasion of his 90th birthda

Are We Seeing Magnetic Axis Reorientation in the Crab and Vela Pulsars?

Variation in the angle $\alpha$ between a pulsar's rotational and magnetic axes would change the torque and spin-down rate. We show that sudden increases in $\alpha$, coincident with glitches, could be responsible for the persistent increases in spin-down rate that follow glitches in the Crab pulsar. Moreover, changes in $\alpha$ at a rate similar to that inferred for the Crab pulsar account naturally for the very low braking index of the Vela pulsar. If $\alpha$ increases with time, all pulsar ages obtained from the conventional braking model are underestimates. Decoupling of the neutron star liquid interior from the external torque cannot account for Vela's low braking index. Variations in the Crab's pulse profile due to changes in $\alpha$ might be measurable.Comment: 14 pages and one figure, Latex, uses aasms4.sty. Accepted to ApJ Letter

Strong laws of large numbers for sub-linear expectations

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.Comment: 10 page

Thermal X-Ray Pulses Resulting From Pulsar Glitches

The non-spherically symmetric transport equations and exact thermal evolution model are used to calculate the transient thermal response to pulsars. The three possible ways of energy release originated from glitches, namely the `shell', `ring' and `spot' cases are compared. The X-ray light curves resulting from the thermal response to the glitches are calculated. Only the `spot' case and the `ring' case are considered because the `shell' case does not produce significant modulative X-rays. The magnetic field ($\vec B$) effect, the relativistic light bending effect and the rotational effect on the photons being emitted in a finite region are considered. Various sets of parameters result in different evolution patterns of light curves. We find that this modulated thermal X-ray radiation resulting from glitches may provide some useful constraints on glitch models.Comment: 48 pages, 20 figures, submitted to Ap