Detecting and Characterizing Small Dense Bipartite-like Subgraphs by the Bipartiteness Ratio Measure

We study the problem of finding and characterizing subgraphs with small \textit{bipartiteness ratio}. We give a bicriteria approximation algorithm \verb|SwpDB| such that if there exists a subset $S$ of volume at most $k$ and bipartiteness ratio $\theta$, then for any $0<\epsilon<1/2$, it finds a set $S'$ of volume at most $2k^{1+\epsilon}$ and bipartiteness ratio at most $4\sqrt{\theta/\epsilon}$. By combining a truncation operation, we give a local algorithm \verb|LocDB|, which has asymptotically the same approximation guarantee as the algorithm \verb|SwpDB| on both the volume and bipartiteness ratio of the output set, and runs in time $O(\epsilon^2\theta^{-2}k^{1+\epsilon}\ln^3k)$, independent of the size of the graph. Finally, we give a spectral characterization of the small dense bipartite-like subgraphs by using the $k$th \textit{largest} eigenvalue of the Laplacian of the graph.Comment: 17 pages; ISAAC 201

Variational study of the antiferromagnetic insulating phase of V2O3 based on Nth order Muffin-Tin-Orbitals

Motivated by recent results of $N$th order muffin-tin orbital (NMTO) implementation of the density functional theory (DFT), we re-examine low-temperature ground-state properties of the anti-ferromagnetic insulating phase of vanadium sesquioxide V$_2$O$_3$. The hopping matrix elements obtained by the NMTO-downfolding procedure differ significantly from those previously obtained in electronic structure calculations and imply that the in-plane hopping integrals are as important as the out-of-plane ones. We use the NMTO hopping matrix elements as input and perform a variational study of the ground state. We show that the formation of stable molecules throughout the crystal is not favorable in this case and that the experimentally observed magnetic structure can still be obtained in the atomic variational regime. However the resulting ground state (two $t_{2g}$ electrons occupying the degenerate $e_g$ doublet) is in contrast with many well established experimental observations. We discuss the implications of this finding in the light of the non-local electronic correlations certainly present in this compound.Comment: 7 pages, 2 figure

Enumeration of chord diagrams on many intervals and their non-orientable analogs

Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent vertices in one model but not in the other. In the former case, we record in a generating function the number of fatgraph boundary cycles containing a fixed number of bivalent vertices while in the latter, we instead record the number of boundary cycles of each fixed length. Second order, non-linear, algebraic partial differential equations are derived which are satisfied by these generating functions in each case giving efficient enumerative schemes. Moreover, these generating functions provide multi-parameter families of solutions to the KP hierarchy. For each model, there is furthermore a non-orientable analog, and each such model likewise has its own associated differential equation. The enumerative problems we solve are interpreted in terms of certain polygon gluings. As specific applications, we discuss models of several interacting RNA molecules. We also study a matrix integral which computes numbers of chord diagrams in both orientable and non-orientable cases in the model with bivalent vertices, and the large-N limit is computed using techniques of free probability.Comment: 23 pages, 7 figures; revised and extended versio

Competing Ordered Phases in URu2Si2: Hydrostatic Pressure and Re-substitution

A persistent kink in the pressure dependence of the \hidden order" (HO) transition temperature of URu2-xRexSi2 is observed at a critical pressure Pc=15 kbar for 0 < x < 0.08. In URu2Si2, the kink at Pc is accompanied by the destruction of superconductivity; a change in the magnitude of a spin excitation gap, determined from electrical resistivity measurements; and a complete gapping of a portion of the Fermi surface (FS), inferred from a change in scattering and the competition between the HO state and superconductivity for FS fraction

GRB Energetics and the GRB Hubble Diagram: Promises and Limitations

We present a complete sample of 29 GRBs for which it has been possible to determine temporal breaks (or limits) from their afterglow light curves. We interpret these breaks within the framework of the uniform conical jet model, incorporating realistic estimates of the ambient density and propagating error estimates on the measured quantities. In agreement with our previous analysis of a smaller sample, the derived jet opening angles of those 16 bursts with redshifts result in a narrow clustering of geometrically-corrected gamma-ray energies about E_gamma = 1.33e51 erg; the burst-to-burst variance about this value is a factor of 2.2. Despite this rather small scatter, we demonstrate in a series of GRB Hubble diagrams, that the current sample cannot place meaningful constraints upon the fundamental parameters of the Universe. Indeed for GRBs to ever be useful in cosmographic measurements we argue the necessity of two directions. First, GRB Hubble diagrams should be based upon fundamental physical quantities such as energy, rather than empirically-derived and physically ill-understood distance indicators. Second, a more homogeneous set should be constructed by culling sub-classes from the larger sample. These sub-classes, though now first recognizable by deviant energies, ultimately must be identifiable by properties other than those directly related to energy. We identify a new sub-class of GRBs (``f-GRBs'') which appear both underluminous by factors of at least 10 and exhibit a rapid fading at early times. About 10-20% of observed long-duration bursts appear to be f-GRBs.Comment: Accepted to the Astrophysical Journal (20 May 2003). 19 pages, 3 Postscript figure

Self-contained Kondo effect in single molecules

Kondo coupling of f and conduction electrons is a common feature of f-electron intermetallics. Similar effects should occur in carbon ring systems(metallocenes). Evidence for Kondo coupling in Ce(C8H8)2 (cerocene) and the ytterbocene Cp*2Yb(bipy) is reported from magnetic susceptibility and L_III-edge x-ray absorption spectroscopy. These well-defined systems provide a new way to study the Kondo effect on the nanoscale, should generate insight into the Anderson Lattice problem, and indicate the importance of this often-ignored contribution to bonding in organometallics.Comment: 4 pages, 5 figures (eps

Experimental Proof of Quantum Nonlocality without Squeezing

It is shown that the ensemble $\{p (\alpha),|\alpha>|\alpha^*>\}$ where $p (\alpha)$ is a Gaussian distribution of finite variance and $| \alpha>$ is a coherent state can be better discriminated with an entangled measurement than with any local strategy supplemented by classical communication. Although this ensemble consists of products of quasi-classical states, it exhibits some quantum nonlocality. This remarkable effect is demonstrated experimentally by implementing the optimal local strategy together with a joint nonlocal strategy that yields a higher fidelity.Comment: 4 pages, 2 figure

Coupled Magnetic Excitations in Single Crystal PrBa2Cu3O6.2

The dispersion of the low-energy magnetic excitations of the Pr sublattice in PrBa2Cu3O6.2 is determined by inelastic neutron scattering measurements on a single crystal. The dispersion, which shows the effect of interactions with the Cu spin-waves, is well described by a model of the coupled Cu-Pr magnetic system. This enables values for the principal exchange constants to be determined, which suggest that both Pr-Pr and Cu-Pr interactions are important in producing the anomalously high ordering temperature of the Pr sublattice. Measurements of the Cu optic spin wave mode show that the inter-layer Cu-Cu exchange is significantly lower than in YBa2Cu3O6.2.Comment: To be published Phys. Rev. Let