On the diffeomorphism commutators of lattice quantum gravity

We show that the algebra of discretized spatial diffeomorphism constraints in Hamiltonian lattice quantum gravity closes without anomalies in the limit of small lattice spacing. The result holds for arbitrary factor-ordering and for a variety of different discretizations of the continuum constraints, and thus generalizes an earlier calculation by Renteln.Comment: 16 pages, Te

Marine diversity shift linked to interactions among grazers, nutrients and propagule banks

Diverse coastal seaweed communities dominated by perennial fucoids become replaced by species-poor turfs of annual algae throughout the Baltic Sea. A large-scale field survey and factorial field experiments indicated that grazers maintain the fucoid community through selective consumption of annual algae. Interactive effects between grazers and dormant propagules of annual algae, stored in a 'marine seed bank', determine the response of this system to anthropogenic nutrient loading. Nutrients override grazer control and accelerate the loss of algal diversity in the presence but not in the absence of a propagule bank. This implies a novel role of propagule banks for community regulation and ecosystem response to marine eutrophication

Universal approximation of multi-copy states and universal quantum lossless data compression

We have proven that there exists a quantum state approximating any multi-copy state universally when we measure the error by means of the normalized relative entropy. While the qubit case was proven by Krattenthaler and Slater (IEEE Trans. IT, 46, 801-819 (2000); quant-ph/9612043), the general case has been open for more than ten years. For a deeper analysis, we have solved the mini-max problem concerning `approximation error' up to the second order. Furthermore, we have applied this result to quantum lossless data compression, and have constructed a universal quantum lossless data compression

Attractive double-layer forces between neutral hydrophobic and neutral hydrophilic surfaces

The interaction between surface patches of proteins with different surface properties has a vital role to play driving conformational changes of proteins in different salt solutions. We demonstrate the existence of ion-specific attractive double-layer forces between neutral hydrophobic and hydrophilic surfaces in the presence of certain salt solutions. This is done by solving a generalized Poisson-Boltzmann equation for two unequal surfaces. In the calculations we utilize parameterized ion-surface-potentials and dielectric-constant-profiles deduced from recent non-primitive-model molecular dynamics (MD) simulations that account partially for molecular structure and hydration effects.Comment: 5 pages, 8 figure

The Spin Holonomy Group In General Relativity

It has recently been shown by Goldberg et al that the holonomy group of the chiral spin-connection is preserved under time evolution in vacuum general relativity. Here, the underlying reason for the time-independence of the holonomy group is traced to the self-duality of the curvature 2-form for an Einstein space. This observation reveals that the holonomy group is time-independent not only in vacuum, but also in the presence of a cosmological constant. It also shows that once matter is coupled to gravity, the "conservation of holonomy" is lost. When the fundamental group of space is non-trivial, the holonomy group need not be connected. For each homotopy class of loops, the holonomies comprise a coset of the full holonomy group modulo its connected component. These cosets are also time-independent. All possible holonomy groups that can arise are classified, and examples are given of connections with these holonomy groups. The classification of local and global solutions with given holonomy groups is discussed.Comment: 21 page

Comparison of the Conceptual Map and Traditional Lecture Methods on Students’ Learning Based on the VARK Learning Style Model: A Randomized Controlled Trial

Developing skills and knowledge in nursing education remains a considerable challenge. Nurse instructors need to be aware of students' learning styles so as to meet students' individual learning preferences and optimize knowledge and understanding. The aim of this study was to compare the effects of the conceptual map and the traditional lecture methods on students' learning based on the VARK learning styles model. In this randomized controlled trial, 160 students from nursing, nurse anesthetics, and midwifery disciplines with four different learning styles of visual, auditory, reading/writing, and kinesthetic were selected using the convenience sampling method. Participants were randomly assigned to the intervention (conceptual map method) or control (traditional lecture method) groups. A medical-surgical nursing course was taught to the students in both groups over 6 weeks. Data collection tools consisted of the VARK questionnaire and pre-and postassessments. Data were analyzed using descriptive and inferential statistics via the SPSS software. Teaching using the conceptual map method had different effects on the students' learning outcomes based on their learning styles. The conceptual map method had a statistically significant impact on the students' learning in the intervention group compared with the control group in the students with a visual learning style (p ¼ .036). No statistically significant differences were reported between the groups in other three learning styles. Nurse instructors should assess students' learning styles based on the VARK model before the application of a particular teaching method to improve the quality of nursing education and facilitate deeper learning

A left-handed simplicial action for euclidean general relativity

An action for simplicial euclidean general relativity involving only left-handed fields is presented. The simplicial theory is shown to converge to continuum general relativity in the Plebanski formulation as the simplicial complex is refined. This contrasts with the Regge model for which Miller and Brewin have shown that the full field equations are much more restrictive than Einstein's in the continuum limit. The action and field equations of the proposed model are also significantly simpler then those of the Regge model when written directly in terms of their fundamental variables. An entirely analogous hypercubic lattice theory, which approximates Plebanski's form of general relativity is also presented.Comment: Version 3. Adds current home address + slight corrections to references of version 2. Version 2 = substantially clarified form of version 1. 29 pages, 4 figures, Latex, uses psfig.sty to insert postscript figures. psfig.sty included in mailing, also available from this archiv

Topological Lattice Gravity Using Self-Dual Variables

Topological gravity is the reduction of general relativity to flat space-times. A lattice model describing topological gravity is developed starting from a Hamiltonian lattice version of B\w F theory. The extra symmetries not present in gravity that kill the local degrees of freedom in $B\wedge F$ theory are removed. The remaining symmetries preserve the geometrical character of the lattice. Using self-dual variables, the conditions that guarantee the geometricity of the lattice become reality conditions. The local part of the remaining symmetry generators, that respect the geometricity-reality conditions, has the form of Ashtekar's constraints for GR. Only after constraining the initial data to flat lattices and considering the non-local (plus local) part of the constraints does the algebra of the symmetry generators close. A strategy to extend the model for non-flat connections and quantization are discussed.Comment: 22 pages, revtex, no figure

Fisher Information for Inverse Problems and Trace Class Operators

This paper provides a mathematical framework for Fisher information analysis for inverse problems based on Gaussian noise on infinite-dimensional Hilbert space. The covariance operator for the Gaussian noise is assumed to be trace class, and the Jacobian of the forward operator Hilbert-Schmidt. We show that the appropriate space for defining the Fisher information is given by the Cameron-Martin space. This is mainly because the range space of the covariance operator always is strictly smaller than the Hilbert space. For the Fisher information to be well-defined, it is furthermore required that the range space of the Jacobian is contained in the Cameron-Martin space. In order for this condition to hold and for the Fisher information to be trace class, a sufficient condition is formulated based on the singular values of the Jacobian as well as of the eigenvalues of the covariance operator, together with some regularity assumptions regarding their relative rate of convergence. An explicit example is given regarding an electromagnetic inverse source problem with "external" spherically isotropic noise, as well as "internal" additive uncorrelated noise.Comment: Submitted to Journal of Mathematical Physic