Non-solvable contractions of semisimple Lie algebras in low dimension

The problem of non-solvable contractions of Lie algebras is analyzed. By means of a stability theorem, the problem is shown to be deeply related to the embeddings among semisimple Lie algebras and the resulting branching rules for representations. With this procedure, we determine all deformations of indecomposable Lie algebras having a nontrivial Levi decomposition onto semisimple Lie algebras of dimension $n\leq 8$, and obtain the non-solvable contractions of the latter class of algebras.Comment: 21 pages. 2 Tables, 2 figure

Cellular automaton model of precipitation/dissolution coupled with solute transport

Precipitation/dissolution reactions coupled with solute transport are modelled as a cellular automaton in which solute molecules perform a random walk on a regular lattice and react according to a local probabilistic rule. Stationary solid particles dissolve with a certain probability and, provided solid is already present or the solution is saturated, solute particles have a probability to precipitate. In our simulation of the dissolution of a solid block inside uniformly flowing water we obtain solid precipitation downstream from the original solid edge, in contrast to the standard reaction-transport equations. The observed effect is the result of fluctuations in solute density and diminishes when we average over a larger ensemble. The additional precipitation of solid is accompanied by a substantial reduction in the relatively small solute concentration. The model is appropriate for the study of the r\^ole of intrinsic fluctuations in the presence of reaction thresholds and can be employed to investigate porosity changes associated with the carbonation of cement.Comment: LaTeX file, 13 pages. To appear in Journal of Statistical Physics (Proceedings of Lattice Gas'94, June 1994, Princeton). Figures available from author. Requests may be submitted by E-mail ([email protected]) or ordinary mail (Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland

Validation and Calibration of Models for Reaction-Diffusion Systems

Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps ($\Delta x$ and $\Delta t$) are varied independently. On the other hand, anisotropy effects due to the symmetries of the discretization lattice prevent the quantitative calibration of models. We introduce a new class of explicit difference methods for numerical integration of diffusion and reaction-diffusion equations, where the dependence on space and time scales occurs naturally. Numerical solutions approach the exact solution of the continuous diffusion equation for finite $\Delta x$ and $\Delta t$, if the parameter $\gamma_N=D \Delta t/(\Delta x)^2$ assumes a fixed constant value, where $N$ is an odd positive integer parametrizing the alghorithm. The error between the solutions of the discrete and the continuous equations goes to zero as $(\Delta x)^{2(N+2)}$ and the values of $\gamma_N$ are dimension independent. With these new integration methods, anisotropy effects resulting from the finite differences are minimized, defining a standard for validation and calibration of numerical solutions of diffusion and reaction-diffusion equations. Comparison between numerical and analytical solutions of reaction-diffusion equations give global discretization errors of the order of $10^{-6}$ in the sup norm. Circular patterns of travelling waves have a maximum relative random deviation from the spherical symmetry of the order of 0.2%, and the standard deviation of the fluctuations around the mean circular wave front is of the order of $10^{-3}$.Comment: 33 pages, 8 figures, to appear in Int. J. Bifurcation and Chao

Contractions of Low-Dimensional Lie Algebras

Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite invariant and semi-invariant quantities are calculated for wide classes of Lie algebras including all low-dimensional Lie algebras. An algorithm that allows one to handle one-parametric contractions is presented and applied to low-dimensional Lie algebras. As a result, all one-parametric continuous contractions for the both complex and real Lie algebras of dimensions not greater than four are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases. Levels and co-levels of low-dimensional Lie algebras are discussed in detail. Properties of multi-parametric and repeated contractions are also investigated.Comment: 47 pages, 4 figures, revised versio

Expansions of algebras and superalgebras and some applications

After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the Inonu-Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32).Comment: Invited lecture delivered at the 'Deformations and Contractions in Mathematics and Physics Workshop', 15-21 January 2006, Mathematisches Forschungsinstitut Oberwolfach, German

Integrating modes of policy analysis and strategic management practice : requisite elements and dilemmas

There is a need to bring methods to bear on public problems that are inclusive, analytic, and quick. This paper describes the efforts of three pairs of academics working from three different though complementary theoretical foundations and intervention backgrounds (i.e., ways of working) who set out together to meet this challenge. Each of the three pairs had conducted dozens of interventions that had been regarded as successful or very successful by the client groups in dealing with complex policy and strategic problems. One approach focused on leadership issues and stakeholders, another on negotiating competitive strategic intent with attention to stakeholder responses, and the third on analysis of feedback ramifications in developing policies. This paper describes the 10 year longitudinal research project designed to address the above challenge. The important outcomes are reported: the requisite elements of a general integrated approach and the enduring puzzles and tensions that arose from seeking to design a wide-ranging multi-method approach

Extensions, expansions, Lie algebra cohomology and enlarged superspaces

After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.Comment: 9 pages. Invited talk delivered at the EU RTN Workshop, Copenhagen, Sep. 15-19 and at the Argonne Workshop on Branes and Generalized Dynamics, Oct. 20-24, 2003. Only change: wrong number of a reference correcte

Human Adipose Tissue-Derived Mesenchymal Stem Cells Abrogate Plasmablast Formation and Induce Regulatory B Cells Independently of T Helper Cells

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Control of human endometrial stromal cell motility by PDGF-BB, HB-EGF and trophoblast-secreted factors

Human implantation involves extensive tissue remodeling at the fetal-maternal interface. It is becoming increasingly evident that not only trophoblast, but also decidualizing endometrial stromal cells are inherently motile and invasive, and likely contribute to the highly dynamic processes at the implantation site. The present study was undertaken to further characterize the mechanisms involved in the regulation of endometrial stromal cell motility and to identify trophoblast-derived factors that modulate migration. Among local growth factors known to be present at the time of implantation, heparin-binding epidermal growth factor-like growth factor (HB-EGF) triggered chemotaxis (directed locomotion), whereas platelet-derived growth factor (PDGF)-BB elicited both chemotaxis and chemokinesis (non-directed locomotion) of endometrial stromal cells. Supernatants of the trophoblast cell line AC-1M88 and of first trimester villous explant cultures stimulated chemotaxis but not chemokinesis. Proteome profiling for cytokines and angiogenesis factors revealed neither PDGF-BB nor HB-EGF in conditioned media from trophoblast cells or villous explants, while placental growth factor, vascular endothelial growth factor and PDGF-AA were identified as prominent secretory products. Among these, only PDGF-AA triggered endometrial stromal cell chemotaxis. Neutralization of PDGF-AA in trophoblast conditioned media, however, did not diminish chemoattractant activity, suggesting the presence of additional trophoblast-derived chemotactic factors. Pathway inhibitor studies revealed ERK1/2, PI3 kinase/Akt and p38 signaling as relevant for chemotactic motility, whereas chemokinesis depended primarily on PI3 kinase/Akt activation. Both chemotaxis and chemokinesis were stimulated upon inhibition of Rho-associated, coiled-coil containing protein kinase. The chemotactic response to trophoblast secretions was not blunted by inhibition of isolated signaling cascades, indicating activation of overlapping pathways in trophoblast-endometrial communication. In conclusion, trophoblast signals attract endometrial stromal cells, while PDGF-BB and HB-EGF, although not identified as trophoblast-derived, are local growth factors that may serve to fine-tune directed and non-directed migration at the implantation site