The stabilizers in a Drinfeld modular group of the vertices of its Bruhat-Tits tree: an elementary approach

Let $K$ be an algebraic function field of one variable with constant field $k$ and let $C$ be the Dedekind domain consisting of all those elements of $K$ which are integral outside a fixed place $\infty$ of $K$. When $k$ is finite the group $GL_2(C)$ plays a central role in the theory of Drinfeld modular curves analagous to that played by $SL_2(Z)$ in the classical theory of modular forms. When $k$ is finite (resp. infinite) we refer to a group $GL_2(C)$ as an arithmetic (resp. non-arithmetic) Drinfeld modular group. Associated with $GL_2(C)$ is its Bruhat-Tits tree, $T$. The structure of the group is derived from that of the quotient graph $GL_2(C)\backslash T$. Using an elementary approach which refers explicitly to matrices we determine the structure of all the vertex stabilizers of $T$. This extends results of Serre, Takahashi and the authors. We also determine all possible valencies of the vertices of $GL_2(C)\backslash T$ for the important special case where $\infty$ has degree 1.Comment: v2: 33 pages, some improvements, title changed, second author's address update

Genuine non-congruence subgroups of Drinfeld modular groups

Let $A$ be the ring of elements in an algebraic function field $K$ over a finite field $F_q$ which are integral outside a fixed place $\infty$. In an earlier paper we have shown that the Drinfeld modular group $G=GL_2(A)$ has automorphisms which map congruence subgroups to non-congruence subgroups. Here we prove the existence of (uncountably many) normal genuine non-congruence subgroups, defined to be those which remain non-congruence under the action of every automorphism of $G$. In addition, for all but finitely many cases we evaluate $ngncs(G)$, the smallest index of a normal genuine non-congruence subgroup of $G$, and compare it to the minimal index of an arbitrary normal non-congruence subgroup.Comment: final version, 22 pages, some improvement

European Option Pricing with Liquidity Shocks

We study the valuation and hedging problem of European options in a market subject to liquidity shocks. Working within a Markovian regime-switching setting, we model illiquidity as the inability to trade. To isolate the impact of such liquidity constraints, we focus on the case where the market is completely static in the illiquid regime. We then consider derivative pricing using either equivalent martingale measures or exponential indifference mechanisms. Our main results concern the analysis of the semi-linear coupled HJB equation satisfied by the indifference price, as well as its asymptotics when the probability of a liquidity shock is small. We then present several numerical studies of the liquidity risk premia obtained in our models leading to practical guidelines on how to adjust for liquidity risk in option valuation and hedging.Comment: 25 pages, 6 figure

Discovery of a Small Central Disk of CO and HI in the Merger Remnant NGC 34

We present CO(1-0) and HI(21-cm) observations of the central region of the wet merger remnant NGC 34. The Combined Array for Research in Millimeter-wave Astronomy (CARMA) observations detect a regularly rotating disk in CO with a diameter of 2.1 kpc and a total molecular hydrogen mass of ($2.1 \pm 0.2) \times10^9~M_\odot$. The rotation curve of this gas disk rises steeply, reaching maximum velocities at 1" (410 pc) from the center. Interestingly, HI observations done with the Karl G. Jansky Very Large Array show that the absorption against the central continuum has the exact same velocity range as the CO in emission. This strongly suggests that the absorbing HI also lies within 1" from the center, is mixed in and corotates with the molecular gas. A comparison of HI absorption profiles taken at different resolutions (5"-45") shows that the spectra at lower resolutions are less deep at the systemic velocity. This provides evidence for HI emission in the larger beams, covering the region from 1 kpc to 9 kpc from the center. The central rapidly rotating disk was likely formed either during the merger or from fall-back material. Lastly, the radio continuum flux of the central source at mm wavelengths ($5.4\pm1.8$ mJy) is significantly higher than expected from an extrapolation of the synchrotron spectrum, indicating the contribution of thermal free-free emission from the central starburst.Comment: Accepted for publication in A

Kinetics of crimp and slope grip in rock climbing

The aim was to investigate differences of the kinetics of the crimp and the slope grip used in rock climbing. Nine cadaver fingers were prepared and fixated with the proximal phalanx in a frame. The superficial (FDS) and deep (FDP) flexor tendons were loaded selectively and together with 40 N in the crimp grip (PIP joint flexed 90°/DIP joint hyperextended) and the slope grip position (<25° flexed/50° flexed respectively). Five different grip sizes were tested and the flexion force which was generated to the grip was measured. In the crimp grip the FDP generated more flexion force in small sized holds whereas the FDS generated more force in the larger holds. During the slope grip the FDP was more effective than the FDS. While both tendons were loaded, the flexion force was always greater during crimp grip compared with the slope grip. The FDP seems to be most important for very small holds using the crimp grip but also during slope grip holds whereas the FDS is more important for larger flat holds

Mode-coupling theory for structural and conformational dynamics of polymer melts

A mode-coupling theory for dense polymeric systems is developed which unifyingly incorporates the segmental cage effect relevant for structural slowing down and polymer chain conformational degrees of freedom. An ideal glass transition of polymer melts is predicted which becomes molecular-weight independent for large molecules. The theory provides a microscopic justification for the use of the Rouse theory in polymer melts, and the results for Rouse-mode correlators and mean-squared displacements are in good agreement with computer simulation results.Comment: 4 pages, 3 figures, Phys. Rev. Lett. in pres

Structure and thermodynamics of colloid-polymer mixtures: a macromolecular approach

The change of the structure of concentrated colloidal suspensions upon addition of non-adsorbing polymer is studied within a two-component, Ornstein-Zernicke based liquid state approach. The polymers' conformational degrees of freedom are considered and excluded volume is enforced at the segment level. The polymer correlation hole, depletion layer, and excess chemical potentials are described in agreement with polymer physics theory in contrast to models treating the macromolecules as effective spheres. Known depletion attraction effects are recovered for low particle density, while at higher densities novel many-body effects emerge which become dominant for large polymers.Comment: 7 pages, 4 figures; to be published in Europhys. Let

Keck Spectroscopy of Two Young Globular Clusters in the Merger Remnant NGC 3921

Low-resolution UV-to-visual spectra of two candidate globular clusters in the merger remnant NGC 3921 are presented. These two clusters of apparent magnitude V = 22.2 (Mv = -12.5) lie at projected distances of ~5 kpc from the center and move with halo-type radial velocities relative to the local galaxy background. Their spectra show strong Balmer absorption lines indicative of main-sequence turnoffs dominated by A-type stars. Comparisons with model-cluster spectra computed by Bruzual & Charlot and others yield cluster ages in the range of 200-530 Myr, and metallicities about solar to within a factor of three. Given their small half-light radii (Reff < 5 pc) and ages corresponding to ~100 core- crossing times, these clusters are gravitationally bound and, hence, indeed young globulars. Assuming that they had Chabrier-type initial mass functions, their estimated current masses are 2.3(+-0.1)x10^6 Msun and 1.5(+-0.1)x10^6 Msun, respectively, or roughly half the mass of omegaCen. Since NGC 3921 itself shows many signs of being a 0.7(+-0.3) Gyr old protoelliptical, these two young globulars of roughly solar metallicity and their many counterparts observed with the Hubble Space Telescope provide supporting evidence that, in the process of forming elliptical-like remnants, major mergers of gas-rich disks can also increase the number of metal-rich globular clusters. (Abridged)Comment: 22 pages, 6 figures, accepted for publication in AJ, July 200

Polarisation dependence of magnetic Bragg scattering in YMn2_2O5_5

The polarisation dependence of the intensity of elastic magnetic scattering from \ymno\ single crystals has been measured at 25 K in magnetic fields between 1 and 9 T. A significant polarisation dependence was observed in the intensities of magnetic satellite reflections, propagation vector \pv=0.5,0,0.25 measured with both the [100] and [010] axes parallel to the common polarisation and applied field direction. The intensity asymmetries $A$ observed in sets of orthorhombicly equivalent reflections show systematic relationships which allow the phase relationship between different components of their magnetic interaction vectors to be determined. They fix the orientation relationships between the small $y$ and $z$ moments on the \mnfp\ and \mntp\ sub-lattices and lend support to the structure reported by Kim et al. It was found that that $A(hkl)\ne A(\bar h\bar k\bar l)$ which suggests that there is a small modulation of the nuclear structure which has the same wave-vector as the magnetic modulation leading to a small nuclear structure factor for the satellite reflections. The differences $A(hkl)- A(\bar h\bar k\bar l)$ observed indicate shifts in the atomic positions of order 0.005 \AA

Artificial Brains and Hybrid Minds

The paper develops two related thought experiments exploring variations on an ‘animat’ theme. Animats are hybrid devices with both artificial and biological components. Traditionally, ‘components’ have been construed in concrete terms, as physical parts or constituent material structures. Many fascinating issues arise within this context of hybrid physical organization. However, within the context of functional/computational theories of mentality, demarcations based purely on material structure are unduly narrow. It is abstract functional structure which does the key work in characterizing the respective ‘components’ of thinking systems, while the ‘stuff’ of material implementation is of secondary importance. Thus the paper extends the received animat paradigm, and investigates some intriguing consequences of expanding the conception of bio-machine hybrids to include abstract functional and semantic structure. In particular, the thought experiments consider cases of mind-machine merger where there is no physical Brain-Machine Interface: indeed, the material human body and brain have been removed from the picture altogether. The first experiment illustrates some intrinsic theoretical difficulties in attempting to replicate the human mind in an alternative material medium, while the second reveals some deep conceptual problems in attempting to create a form of truly Artificial General Intelligence