Tafassasset: The Saga Continues

In this study, we compare data for two separate Tafassasset stones and supply new oxygen isotope data for our sample. We include a discussion of the debate surrounding the classification of Tafassasset and offer a hypothesis for its origin based upon new information

Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature

We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an arbitrary number of discrete hierarchies of the broken replica symmetry. We show that all solutions with finite-many hierarchies are unstable and only the scheme with infinite-many hierarchies becomes marginally stable. We show how the solutions from the discrete replica-symmetry-breaking scheme go over to the continuous one with increasing the number of hierarchies.Comment: REVTeX4, 11 pages, no figure

Distinctive Identity Claims in Federal Systems: Judicial Policing of Subnational Variance

It is characteristic of federal states that the scope of subnational power and autonomy are subjects of frequent dispute, and that disagreements over the reach of national and subnational power may be contested in a wide and diverse array of settings. Subnational units determined to challenge nationally-imposed limits on their power typically have at their disposal many tools with which to press against formal boundaries. Federal systems, moreover, frequently display a surprising degree of tolerance for subnational obstruction, disobedience, and other behaviors intended to expand subnational authority and influence, even over national objection. This tolerance, however, has limits. In this paper, we examine a set of rulings by national constitutional courts invalidating formalized claims by subnational units to a distinctive subnational identity. The emphatically negative reactions of these courts contrast instructively with the tolerance often displayed by other state actors toward similar identity claims when they are asserted in political and sub-constitutional settings, suggesting that the legal formalization of distinctive identity claims is perceived by courts to pose an unusually acute threat to the state

Sustainable Decentralization: Power, Extraconstitutional Influence, and Subnational Symmetry in the United States and Spain

In the Madisonian tradition of constitutional design, the foundation of a sustainable federalism is thought to be a scientifically precise balancing of national and subnational power. Experience shows, however, that national and subnational actors in highly diverse systems are capable of developing a rich array of extraconstitutional methods of mutual influence, so that the formal, constitutionalized balance of power rarely settles the question of the actual balance of power between levels of government. A more important factor in ensuring the long-term sustainability of a meaningfully federal system is the degree of symmetry across subnational units in their relation to the central state. A comparison of the U.S. and Spain suggests that federalism is most directly threatened when subnational units compete not collectively with the central state, thereby checking its power, but with each other, a condition that furnishes the central state with opportunities to exploit subnational rivalries in ways that risk genuine, long-term destabilization

Rolling balls and Octonions

In this semi-expository paper we disclose hidden symmetries of a classical nonholonomic kinematic model and try to explain geometric meaning of basic invariants of vector distributions

Spin-exchange relaxation free magnetometry with Cs vapor

We describe a Cs atomic magnetometer operating in the spin-exchange relaxation-free (SERF) regime. With a vapor cell temperature of $103^\circ\rm{C}$ we achieve intrinsic magnetic resonance widths $\Delta B=17 {\rm \mu G}$ corresponding to an electron spin-relaxation rate of $300 {\rm s^{-1}}$ when the spin-exchange rate is $\Gamma_{SE}=14000 {\rm s^{-1}}$. We also observe an interesting narrowing effect due to diffusion. Signal-to-noise measurements yield a sensitivity of about $400\thinspace{\rm pG/\sqrt{Hz}}$. Based on photon shot noise, we project a sensitivity of $40 {\rm pG/\sqrt{Hz}}$. A theoretical optimization of the magnetometer indicates sensitivities on the order of $2 {\rm pG/\sqrt{Hz}}$ should be achievable in a $1 {\rm cm^3}$ volume. Because Cs has a higher saturated vapor pressure than other alkali metals, SERF magnetometers using Cs atoms are particularly attractive in applications requiring lower temperatures.Comment: 8 pages, 6 figures. submitted to PR

Linear Superposition in Nonlinear Equations

Even though the KdV and modified KdV equations are nonlinear, we show that suitable linear combinations of known periodic solutions involving Jacobi elliptic functions yield a large class of additional solutions. This procedure works by virtue of some remarkable new identities satisfied by the elliptic functions.Comment: 7 pages, 1 figur

Large Deviation Property of Free Energy in p-Body Sherrington-Kirkpatrick Model

Cumulant generating function phi(n) and rate function Sigma(f) of the free energy is evaluated in p-body Sherrington-Kirkpatrick model by using the replica method with the replica number n finite. From a perturbational argument, we show that the cumulant generating function is constant in the vicinity of n = 0. On the other hand, with the help of two analytic properties of phi(n), the behavior of phi(n) is derived again. However this is also shown to be broken at a finite value of n, which gives a characteristic value in the rate function near the thermodynamic value of the free energy. Through the continuation of phi(n) as a function of n, we find out a way to derive the 1RSB solution at least in this model, which is to fix the RS solution to be a monotone increasing function.Comment: 7 pages, 5 figures. accepted for publication in J.Phs.Soc.Jp

Two 2MASS-Selected Young Stellar Clusters: Photometry, Spectroscopy, and the IMF

We present near-infrared J, H, and K_s images and K-band spectroscopy of two newly discovered stellar clusters at different stages of evolution. Our spectra suggest the presence of massive YSOs in the heavily embedded cluster in the star-forming region near radio source G353.4-0.4 and an O5-O6V star in the cluster near radio source G305+00.2. We determine a K-band luminosity function (KLF) for both clusters and an initial mass function (IMF) for the cluster near G305+00.2. The derived IMF slope is -1.5 if the KLF is used to derive the IMF and is -0.98 if the color-magnitude diagram and spectra are used. The more reliable CMD-based slope is flatter than the Salpeter value usually found for stellar clusters. We find that using the KLF alone to derive an IMF is likely to produce an overly steep slope in stellar clusters subject to variable extinction.Comment: 16 pages, 18 figures, accepted to A

Serially-regulated biological networks fully realize a constrained set of functions

We show that biological networks with serial regulation (each node regulated by at most one other node) are constrained to {\it direct functionality}, in which the sign of the effect of an environmental input on a target species depends only on the direct path from the input to the target, even when there is a feedback loop allowing for multiple interaction pathways. Using a stochastic model for a set of small transcriptional regulatory networks that have been studied experimentally, we further find that all networks can achieve all functions permitted by this constraint under reasonable settings of biochemical parameters. This underscores the functional versatility of the networks.Comment: 9 pages, 3 figure