Abstract:
We prove that the Gauss map of a surface of constant mean curvature embedded in Minkowski space is harmonic. This fact will then be used to study 2+1 gravity for surfaces of genus higher than one. By considering the energy of the Gauss map, a canonical transform between the ADM reduced variables and holonomy variables can be constructed. This allows one to solve (in principle) for the evolution in the ADM variables without having to explicitly solve the constraints first.

Abstract:
The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability and robustness of a large class of dynamics on such networks. We determine the probability distribution of robustness as a function of network topology and show that robustness is classified by the number of links between modules of the network. We also demonstrate that permutation of these modules is a fundamental symmetry of dynamical robustness. Analysis of these findings leads to the conclusion that the most robust systems have the most hierarchical structure. This relationship provides a means by which evolutionary selection for a purely dynamical phenomenon may shape network architectures across scales of the biological hierarchy.

Abstract:
Constraints placed upon the phenotypes of organisms result from their interactions with the environment. Over evolutionary timescales, these constraints feed back onto smaller molecular subnetworks comprising the organism. The evolution of biological networks is studied by considering a network of a few nodes embedded in a larger context. Taking into account this fact that any network under study is actually embedded in a larger context, we define network architecture, not on the basis of physical interactions alone, but rather as a specification of the manner in which constraints are placed upon the states of its nodes. We show that such network architectures possessing cycles in their topology, in contrast to those that do not, may be subjected to unsatisfiable constraints. This may be a significant factor leading to selection biased against those network architectures where such inconsistent constraints are more likely to arise. We proceed to quantify the likelihood of inconsistency arising as a function of network architecture finding that, in the absence of sampling bias over the space of possible constraints and for a given network size, networks with a larger number of cycles are more likely to have unsatisfiable constraints placed upon them. Our results identify a constraint that, at least in isolation, would contribute to a bias in the evolutionary process toward more hierarchical-modular versus completely connected network architectures. Together, these results highlight the context-dependence of the functionality of biological networks.

Abstract:
This work consists of two distinct parts. In the first part we present a new method for solving the initial value problem of general relativity. Given any spatial metric with a surface orthogonal Killing field and two freely specified components of the extrinsic curvature we solve for extrinsic curvature's remaining components. For the second part, after noting that initial data for the Kerr spacetime can be derived within our formalism we construct data for axisymmetric configurations of spinning black holes. Though our method is limited to axisymmetry, it offers an advantage over the Bowen-York proceedure that our data approach those for Kerr holes in the limit of large separations and in the close limit.

Abstract:
We point out the existence of new effects of global spacetime expansion on local binary systems. In addition to a possible change of orbital size, there is a contribution to the precession of elliptic orbits, to be added to the well-known general relativistic effect in static spacetimes, and the eccentricity can change. Our model calculations are done using geodesics in a McVittie metric, representing a localized system in an asymptotically Robertson-Walker spacetime; we give a few numerical estimates for that case, and indicate ways in which the model should be improved.

Abstract:
Voltage-gated sodium channels (VGSCs) contain a specific binding site for a family of cone shell toxins known as μ-conotoxins. As some VGSCs are involved in pain perception and μ-conotoxins are able to block these channels, μ-conotoxins show considerable potential as analgesics. Recent studies have advanced our understanding of the three-dimensional structures and structure-function relationships of the μ-conotoxins, including their interaction with VGSCs. Truncated peptide analogues of the native toxins have been created in which secondary structure elements are stabilized by non-native linkers such as lactam bridges. Ultimately, it would be desirable to capture the favourable analgesic properties of the native toxins, in particular their potency and channel sub-type selectivity, in non-peptide mimetics. Such mimetics would constitute lead compounds in the development of new therapeutics for the treatment of pain.

Abstract:
The Debrecen workshop was one of a number held in preparation for the UNESCO-ICSU World Conference on Science, which will be held in Budapest, June 1999. A report representing the views of the workshop, prepared for that conference and containing a number of recommended actions, is included with this summary. The workshop affirmed the ongoing importance of physics for its own sake and as part of our culture, as a key element in our increasingly unified science and as an essential contributor to the solution of environmental and energy problems. The problems faced by physics as an activity and as an educational subject were discussed and actions for both society as a whole and the physics community itself were put forward.

Abstract:
In what follows we first set the context for inverse scattering in nuclear physics with a brief account of inverse problems in general. We then turn to inverse scattering which involves the S-matrix, which connects the interaction potential between two scattering particles with the measured scattering cross section. The term `inverse' is a reference to the fact that instead of determining the scattering S-matrix from the interaction potential between the scattering particles, we do the inverse. That is to say, we calculate the interaction potential from the S-matrix. This review explains how this can now be done reliably, but the emphasis will be upon reasons why one should wish to do this, with an account of some of the ways this can lead to understanding concerning nuclear interactions.

Abstract:
Inelastic neutron scattering was used to study the low energy magnetic excitations of the ferromagnetic superconductor UGe$_{2}$. The ferromagnetic fluctuations are of Ising nature with a non-conserved magnetization and have an intermediate behavior between localized and itinerant magnetism.

Abstract:
It is shown by detailed inelastic neutron scattering experiments that the gapped collective magnetic excitation of the unconventional superconductor CeCoIn$_{5}$, the spin resonance mode, is incommensurate and that the corresponding fluctuations are of Ising nature. The incommensurate peak position of these fluctuations corresponds to the propagation vector of the adjacent field induced static magnetic ordered phase, the so-called Q-phase. Furthermore, the direction of the magnetic moment fluctuations is also the direction of the ordered magnetic moments of the Q-phase. Hence the resonance mode and the Q-phase share the same symmetry and this strongly supports a scenario where the static order is realized by a condensation of the magnetic excitation.