Monotonicity of Degrees of Generalized Alexander Polynomials of Groups and 3-Manifolds

We investigate the behavior of the higher-order degrees, db_n, of a finitely presented group G. These db_n are functions from H^1(G;Z) to Z whose values are the degrees certain higher-order Alexander polynomials. We show that if def(G) is at least 1 or G is the fundamental group of a compact, orientable 3-manifold then db_n is a monotonically increasing function of n for n at least 1. This is false for general groups. As a consequence, we show that if a 4 manifold of the form X times S^1 admits a symplectic structure then X ``looks algebraically like'' a 3-manifold that fibers over S^1, supporting a positive answer to a question of Taubes. This generalizes a theorem of S. Vidussi and is an improvement on the previous results of the author. We also find new conditions on a 3-manifold X which will guarantee that the Thurston norm of f*(psi), for psi in H^1(X;\Z) and f:Y -> X a surjective map on pi_1, will be at least as large the Thurston norm of psi. When X and Y are knot complements, this gives a partial answer to a question of J. Simon. More generally, we define Gamma-degrees, db_Gamma, corresponding to a surjective map G -> Gamma for which Gamma is poly-torsion-free-abelian. Under certain conditions, we show they satisfy a monotonicity condition if one varies the group. As a result, we show that these generalized degrees give obstructions to the deficiency of a group being positive and obstructions to a finitely presented group being the fundamental group of a compact, orientable 3-manifold.Comment: 19 page

On the Cut Number of a 3-manifold

The question was raised as to whether the cut number of a 3-manifold X is bounded from below by 1/3 beta_1(X). We show that the answer to this question is `no.' For each m>0, we construct explicit examples of closed 3-manifolds X with beta_1(X)=m and cut number 1. That is, pi_1(X) cannot map onto any non-abelian free group. Moreover, we show that these examples can be assumed to be hyperbolic.Comment: Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper15.abs.htm

Molecular Dynamics Simulations of a Pressure-induced Glass Transition

We simulate the compression of a two-component Lennard-Jones liquid at a variety of constant temperatures using a molecular dynamics algorithm in an isobaric-isothermal ensemble. The viscosity of the liquid increases with pressure, undergoing a broadened transition into a structurally arrested, amorphous state. This transition, like the more familiar one induced by cooling, is correlated with a significant increase in icosahedral ordering. In fact, the structure of the final state, as measured by an analysis of the bonding, is essentially the same in the glassy, frozen state whether produced by squeezing or by cooling under pressure. We have computed an effective hard-sphere packing fraction at the transition, defining the transition pressure or temperature by a cutoff in the diffusion constant, analogous to the traditional laboratory definition of the glass transition by an arbitrary, low cutoff in viscosity. The packing fraction at this transition point is not constant, but is consistently higher for runs compressed at higher temperature. We show that this is because the transition point defined by a constant cutoff in the diffusion constant is not the same as the point of structural arrest, at which further changes in pressure induce no further structural changes, but that the two alternate descriptions may be reconciled by using a thermally activated cutoff for the diffusion constant. This enables estimation of the characteristic activation energy for diffusion at the point of structural arrest.Comment: Latex using Revtex macro

The BCS theory of q-deformed nucleon pairs - qBCS

We construct a coherent state of q-deformed zero coupled nucleon pairs distributed in several single-particle orbits. Using a variational approach, the set of equations of qBCS theory, to be solved self consistently for occupation probabilities, gap parameter Delta, and the chemical potential lambda, is obtained. Results for valence nucleons in nuclear degenerate sdg major shell show that the strongly coupled zero angular momentum nucleon pairs can be substituted by weakly coupled q-deformed zero angular momentum nucleon pairs. A study of Sn isotopes reveals a well defined universe of (G, q) values, for which qBCS converges. While the qBCS and BCS show similar results for Gap parameter Delta in Sn isotopes, the ground state energies are lower in qBCS. The pairing correlations in N nucleon system, increase with increasing q (for q real).Comment: 8 pages, REVTEX, 3 eps figure

Endogenous Wnt signalling in human embryonic stem cells generates an equilibrium of distinct lineage-specified progenitors.

The pluripotent nature of human embryonic stem cells (hESCs) makes them convenient for deriving therapeutically relevant cells. Here we show using Wnt reporter hESC lines that the cells are heterogeneous with respect to endogenous Wnt signalling activity. Moreover, the level of Wnt signalling activity in individual cells correlates with differences in clonogenic potential and lineage-specific differentiation propensity. The addition of Wnt protein or, conversely, a small-molecule Wnt inhibitor (IWP2) reduces heterogeneity, allowing stable expansion of Wnt(high) or Wnt(low) hESC populations, respectively. On differentiation, the Wnt(high) hESCs predominantly form endodermal and cardiac cells, whereas the Wnt(low) hESCs generate primarily neuroectodermal cells. Thus, heterogeneity with respect to endogenous Wnt signalling underlies much of the inefficiency in directing hESCs towards specific cell types. The relatively uniform differentiation potential of the Wnt(high) and Wnt(low) hESCs leads to faster and more efficient derivation of targeted cell types from these populations

Getting In On the Act: How Arts Groups are Creating Opportunities for Active Participation

Arts participation is being redefined as people increasingly choose to engage with art in new, more active and expressive ways. This movement carries profound implications, and fresh opportunities, for the nonprofit arts sector.We are in the midst of a seismic shift in cultural production, moving from a "sit-back-and-be-told culture" to a "making-and-doing-culture." Active or participatory arts practices are emerging from the fringes of the Western cultural tradition to capture the collective imagination. Many forces have conspired to lead us to this point. The sustained economic downturn that began in 2008, rising ticket prices, the pervasiveness of social media, the roliferation of digital content and rising expectations for self-guided, on-demand, customized experiences have all contributed to a cultural environment primed for active arts practice. This shift calls for a new equilibrium in the arts ecology and a new generation of arts leaders ready to accept, integrate and celebrate all forms of cultural practice. This is, perhaps, the defining challenge of our time for artists, arts organizations and their supporters -- to embrace a more holistic view of the cultural ecology and identify new possibilities for Americans to engage with the arts.How can arts institutions adapt to this new environment?Is participatory practice contradictory to, or complementary to, a business model that relies on professional production and consumption?How can arts organizations enter this new territory without compromising their values r artistic ideals?This report aims to illuminate a growing body of practice around participatory engagement (with various illustrative case studies profiled at the end) and dispel some of the anxiety surrounding this sphere of activity

Scissors Modes and Spin Excitations in Light Nuclei including ΔN\Delta N=2 excitations: Behaviour of 8Be^8Be and 10Be^{10}Be

Shell model calculations are performed for magnetic dipole excitations in $^8{Be}$ and $^{10}{Be}$ in which all valence configurations plus $2\hbar\omega$ excitations are allowed (large space). We study both the orbital and spin excitations. The results are compared with the `valence space only' calculations (small space). The cumulative energy weighted sums are calculated and compared for the $J=0^+$ $T$=0 to $J=1^+$ $T$=1 excitations in $^8{Be}$ and for $J=0^+$ $T$=1 to both $J=1^+$ $T$=1 and $J$=$1^+$ $T$=2 excitations in $^{10}{Be}$. We find for the $J=0^+$ $T$=1 to $J=1^+$ $T$=1 isovector {\underline {spin}} transitions in $^{10}{Be}$ that the summed strength in the {\underline {large}} space is less than in the {\underline {small}} space. We find that the high energy energy-weighted isovector orbital strength is smaller than the low energy strength for transitions in which the isospin is changed, but for $J=0^+$ $T$=1 to $J=1^+$ $T$=1 in $^{10}{Be}$ the high energy strength is larger. We find that the low lying orbital strength in $^{10}{Be}$ is anomalously small, when an attempt is made to correlate it with the $B(E2)$ strength to the lowest $2^+$ states. On the other hand a sum rule of Zheng and Zamick which concerns the total $B(E2)$ strength is reasonably satisfied in both $^8{Be}$ and $^{10}{Be}$. The Wigner supermultiplet scheme is a useful guide in analyzing shell model results. In $^{10}Be$ and with a $Q \cdot Q$ interaction the T=1 and T=2 scissors modes are degenerate, with the latter carrying 5/3 of the T=1 strength.Comment: 51 pages, latex, 9 figures available upon reques

Using National Measures of Patients' Perceptions of Health Care to Design and Debrief Clinical Simulations

This article describes an innovative approach to using national measures of patients' perspectives of quality health care. Nurses from a regional simulation consortium designed and executed a simulation using the Hospital Consumer Assessment of Healthcare Providers and Systems (HCAHPS) survey to prepare nurses to improve care and, in turn, enhance patients' perceptions of care. The consortium is currently revising the reporting mechanism to collect data about specific learning objectives based on national quality indicator benchmarks, specifically HCAHPS. This revision reflects the changing needs of health care to include quality metrics in simulation