Stable Marriage with Multi-Modal Preferences

We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one "evaluation mode" (e.g., more than one criterion); thus, each agent is equipped with multiple preference lists, each ranking the counterparts in a possibly different way. We introduce and study three natural concepts of stability, investigate their mutual relations and focus on computational complexity aspects with respect to computing stable matchings in these new scenarios. Mostly encountering computational hardness (NP-hardness), we can also spot few islands of tractability and make a surprising connection to the \textsc{Graph Isomorphism} problem

Approximability results for stable marriage problems with ties

We consider instances of the classical stable marriage problem in which persons may include ties in their preference lists. We show that, in such a setting, strong lower bounds hold for the approximability of each of the problems of finding an egalitarian, minimum regret and sex-equal stable matching. We also consider stable marriage instances in which persons may express unacceptable partners in addition to ties. In this setting, we prove that there are constants delta, delta' such that each of the problems of approximating a maximum and minimum cardinality stable matching within factors of delta, delta' (respectively) is NP-hard, under strong restrictions. We also give an approximation algorithm for both problems that has a performance guarantee expressible in terms of the number of lists with ties. This significantly improves on the best-known previous performance guarantee, for the case that the ties are sparse. Our results have applications to large-scale centralized matching schemes

Current-driven Magnetization Reversal in a Ferromagnetic Semiconductor (Ga,Mn)As/GaAs/(Ga,Mn)As Tunnel Junction

Current-driven magnetization reversal in a ferromagnetic semiconductor based (Ga,Mn)As/GaAs/(Ga,Mn)As magnetic tunnel junction is demonstrated at 30 K. Magnetoresistance measurements combined with current pulse application on a rectangular 1.5 x 0.3 um^2 device revealed that magnetization switching occurs at low critical current densities of 1.1 - 2.2 x 10^5 A/cm^2 despite the presence of spin-orbit interaction in the p-type semiconductor system. Possible mechanisms responsible for the effect are discussed.Comment: 16 pages, 4 figure

Structure and magnetism in nanocrystalline Ca(La)B6_6 films

Nanocrystalline films of La-doped CaB$_6$ have been fabricated by using a rf-magnetron sputtering. Lattice expansion of up to 6% with respect to the bulk value was observed along the direction perpendicular to the film plane, which arises from the trapping of Ar gas into the film. Large ferromagnetic moment of 3 ~ 4 Bohr magneton per La has been observed in some La-doped films only when the lattice expansion rate is larger than 2.5%.Comment: 2 pages, 2 figures, to appear in J. Magn. Magn. Mate

Shot Noise in Magnetic Tunnel Junctions: Evidence for Sequential Tunneling

We report the experimental observation of sub-Poissonian shot noise in single magnetic tunnel junctions, indicating the importance of tunneling via impurity levels inside the tunnel barrier. For junctions with weak zero-bias anomaly in conductance, the Fano factor (normalized shot noise) depends on the magnetic configuration being enhanced for antiparallel alignment of the ferromagnetic electrodes. We propose a model of sequential tunneling through nonmagnetic and paramagnetic impurity levels inside the tunnel barrier to qualitatively explain the observations.Comment: 5 pages, 5 figure

Subaru Deep Survey VI. A Census of Lyman Break Galaxies at z=4 and 5 in the Subaru Deep Fields: Clustering Properties

We investigate the clustering properties of 2,600 Lyman Break Galaxies (LBGs) at z=3.5-5.2 in two large blank fields, the Subaru Deep Field and the Subaru/XMM Deep Field (600arcmin^2 each). The angular correlation functions of these LBGs show a clear clustering at both z~4 and 5. The correlation lengths are r_0= 4.1^{+0.2}_{-0.2} and 5.9^{+1.3}_{-1.7} h_{100}^{-1} Mpc (r_0= 5.1^{+1.0}_{-1.1} and 5.9^{+1.3}_{-1.7} h_{100}^{-1} Mpc) for all the detected LBGs (for L>L* LBGs) at z~4 and 5, respectively. These correlation lengths correspond to galaxy-dark matter biases of b_g= 2.9^{+0.1}_{-0.1} and 4.6^{+0.9}_{-1.2} (b_g=3.5^{+0.6}_{-0.7} and 4.6^{+0.9}_{-1.2}), for all the detected LBGs (for L>L^* LBGs) at z~4 and 5, respectively. These results, combined with estimates for z~3 LBGs in the literature, show that the correlation length of L>L^* LBGs is almost constant, ~5 h_{100}^{-1} Mpc, over z~3-5, while the bias monotonically increases with redshift at z>3. We also find that for LBGs at z~4 the clustering amplitude increases with UV-continuum luminosity and with the amount of dust extinction. We estimate the mass of dark halos hosting various kinds of high-z galaxies including LBGs with the analytic model given by Sheth & Tormen (1999). We find that the typical mass of dark halos hosting L>L^* LBGs is about 1x10^{12} h_{70}^{-1}Msol over z~3-5, which is comparable to that of the Milky Way Galaxy. A single dark halo with ~10^{12} h_{70}^{-1} Msol is found to host 0.1-0.3 LBG on average but host about four K-band selected galaxies.Comment: 33 pages, 12 figures, ApJ in press. Paper with high resolution figures is available at http://hikari.astron.s.u-tokyo.ac.jp/~ouchi/work/astroph/SDS_V_VI/SDS_VI.pdf (PDF) (The abstract was reduced by the revision.

Isotope labeling strategies for NMR studies of RNA

The known biological functions of RNA have expanded in recent years and now include gene regulation, maintenance of sub-cellular structure, and catalysis, in addition to propagation of genetic information. As for proteins, RNA function is tightly correlated with structure. Unlike proteins, structural information for larger, biologically functional RNAs is relatively limited. NMR signal degeneracy, relaxation problems, and a paucity of long-range 1H–1H dipolar contacts have limited the utility of traditional NMR approaches. Selective isotope labeling, including nucleotide-specific and segmental labeling strategies, may provide the best opportunities for obtaining structural information by NMR. Here we review methods that have been developed for preparing and purifying isotopically labeled RNAs, as well as NMR strategies that have been employed for signal assignment and structure determination

Unknotting numbers and triple point cancelling numbers of torus-covering knots

It is known that any surface knot can be transformed to an unknotted surface knot or a surface knot which has a diagram with no triple points by a finite number of 1-handle additions. The minimum number of such 1-handles is called the unknotting number or the triple point cancelling number, respectively. In this paper, we give upper bounds and lower bounds of unknotting numbers and triple point cancelling numbers of torus-covering knots, which are surface knots in the form of coverings over the standard torus $T$. Upper bounds are given by using $m$-charts on $T$ presenting torus-covering knots, and lower bounds are given by using quandle colorings and quandle cocycle invariants.Comment: 26 pages, 14 figures, added Corollary 1.7, to appear in J. Knot Theory Ramification