Diversity of graphs with highly variable connectivity

A popular approach for describing the structure of many complex networks focuses on graph theoretic properties that characterize their large-scale connectivity. While it is generally recognized that such descriptions based on aggregate statistics do not uniquely characterize a particular graph and also that many such statistical features are interdependent, the relationship between competing descriptions is not entirely understood. This paper lends perspective on this problem by showing how the degree sequence and other constraints (e.g., connectedness, no self-loops or parallel edges) on a particular graph play a primary role in dictating many features, including its correlation structure. Building on recent work, we show how a simple structural metric characterizes key differences between graphs having the same degree sequence. More broadly, we show how the (often implicit) choice of a background set against which to measure graph features has serious implications for the interpretation and comparability of graph theoretic descriptions

High temperature expansion applied to fermions near Feshbach resonance

We show that, apart from a difference in scale, all of the surprising recently observed properties of a degenerate Fermi gas near a Feshbach resonance persist in the high temperature Boltzmann regime. In this regime, the Feshbach resonance is unshifted. By sweeping across the resonance, a thermal distribution of bound states (molecules) can be reversibly generated. Throughout this process, the interaction energy is negative and continuous. We also show that this behavior must persist at lower temperatures unless there is a phase transition as the temperature is lowered. We rigorously demonstrate universal behavior near the resonance.Comment: 4 pages, 4 figures (3 color, 1 BW), RevTeX4; ver4 -- updated references, changed title -- version accepted for publication in Physical Review Letter

Rapidly Rotating Fermi Gases

We show that the density profile of a Fermi gas in rapidly rotating potential will develop prominent features reflecting the underlying Landau level like energy spectrum. Depending on the aspect ratio of the trap, these features can be a sequence of ellipsoidal volumes or a sequence of quantized steps.Comment: 4 pages, 1 postscript fil

Fermion Superfluids of Non-Zero Orbital Angular Momentum near Resonance

We study the pairing of Fermi gases near the scattering resonance of the $\ell\neq 0$ partial wave. Using a model potential which reproduces the actual two-body low energy scattering amplitude, we have obtained an analytic solution of the gap equation. We show that the ground state of $\ell=1$ and $\ell=3$ superfluid are orbital ferromagnets with pairing wavefunctions $Y_{11}$ and $Y_{32}$ respectively. For $\ell=2$, there is a degeneracy between $Y_{22}$ and a "cyclic state". Dipole energy will orient the angular momentum axis. The gap function can be determined by the angular dependence of the momentum distribution of the fermions.Comment: 4 pages, 1 figur

Digital entertainment entrepreneurship laboratory in the network economy

Thesis (M. Arch.)--Massachusetts Institute of Technology, Dept. of Architecture, 1999.Includes bibliographical references (p. 33).The dual phenomena of the information revolution and the rise of the network economy presents an interesting challenge to the architect. Architecture must shift away from the design of singular buildings, and more towards the design of instances (nodes) on a network - and indeed, the design of that network itself. This entails redefining the role of the architect, to introduce the profession into areas not traditionally though of as the architect's domain. It also demands an understanding of the unique social and economic characteristics of the informational society at the conceptual level, in order to define the correct priorities in physical design. The project is a business incubator located at the Burbank-Pasadena-Glendale Airport, in Burbank, California. The incubator is a collective work space that nurtures start-up companies involved in high tech entertainment research and development - for example, digital compositing, robotic prototypes, and advanced visual effects. In addition to providing funding and facilities, the incubator also gives member firms access to local and regional social/information networks. Local entertainment companies, such as Disney and Warner Bros., sponsor the incubator in exchange for the first right to use any technologies developed there, and to contract incubator firms to work for them. Five Organizing Principles: 1: Collective action. The inclusive aspect heightens creative cross-pollination, and transforms the nature of work from a top-down, rational, domination-based hierarchy to a collaborative, serendipitous, cooperative venture. 2: Synchronicity. The juxtaposition of unrelated uses, an architecture that reinforces chance interactions. 3: Juxtaposition of material + speed. Visual overlaps and juxtapositions highlight the multiple velocities and rhythms that permeate our lives, from the eternal to the instantaneous, reflecting the contradictions in speed in our own lives. 4: Architecture as a device. The autonomy of a building/organization is inextricably linked with its absolute dependence on connections to other buildings/organizations, for context, purpose, meaning and productive capacity. 5: Mapping of digital space onto physical space. Architecture has the opportunity to reevaluate the relationship between technology and (human) nature, to recombine and negotiate new concepts of rights, privileges, and access based on the interplay of digital fluidity and physical solidity.CDROM in Apple Macintosh HFS format; MacOS 8.0 or higher; Netscape Navigator 4.0 or higher or Microsoft Internet Explorer 4.0 or higher.by Allen L. Tsai.M.Arch

Which Constituent Quark Model Is Better?

A comparative study has been done by calculating the effective baryon-baryon interactions of the 64 lowest channels consisting of octet and decuplet baryons with three constituent quark models: the extended quark gluon exchange model, the Goldstone boson exchange model and the quark gluon meson exchange hybrid model. We find that these three models give similar results for 44 channels. Further tests of these models are discussed.Comment: 6pp., 3 figs., Asia-Pacific Few-Body Conf. II (Shanghai, Aug.25-30 2002), to appear in MPLA; references adde

SCOZA for Monolayer Films

We show the way in which the self-consistent Ornstein-Zernike approach (SCOZA) to obtaining structure factors and thermodynamics for Hamiltonian models can best be applied to two-dimensional systems such as thin films. We use the nearest-neighbor lattice gas on a square lattice as an illustrative example.Comment: 10 pages, 5 figure