Configurations of flags and representations of surface groups in complex hyperbolic geometry

In this work, we describe a set of coordinates on the PU(2,1)-representation variety of the fundamental group of an oriented punctured surface Σ with negative Euler characteristic. The main technical tool we use is a set of geometric invariants of a triple of flags in the complex hyperbolic plane H²_{\mathbb C}{\bf H^2_{\mathbb {C}}} . We establish a bijection between a set of decorations of an ideal triangulation of Σ and a subset of the PU(2,1)-representation variety of π ₁(Σ).     

A Fleming–Viot Particle Representation¶of the Dirichlet Laplacian

We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. For large N, the particle distribution density converges to the normalized heat equation solution in D with Dirichlet boundary conditions. The stationary distributions converge as N→∞ to the first eigenfunction of the Laplacian in D with the same boundary conditions. Received: 11 November 1999 / Accepted: 19 May 2000     

Legendre transform of the noninteracting kinetic energy: Especially from March–Murray perturbation theory based on plane waves

The Legendre transform of the noninteracting kinetic energy is derived from the March–Murray perturbation theory based on plane waves. Further useful relations are summarized, and it is shown that insight can be gained from simple model systems where nonperturbative equations can be derived. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 138–142, 2001     

Kinetic energy density in terms of electron density for closed-shell atoms in a bare Coulomb field

A long-term aim in density functional theory is to obtain the kinetic energy density t(r) in terms of the ground-state electron density ρ(r). Here, t(r) is written explicitly in terms of ρ(r) for an arbitrary number 𝒩 of closed shells in a bare Coulomb field. In the limit as 𝒩→∞, closed results for t(r) follow from the earlier analysis of ρ(r) by Heilmann and Lieb. [Phys. Rev. A 52 , 3628 (1995)]. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 281–283, 1998     

Exact exchange—correlation potential from low-order density matrices

The local energy equation derived by Dawson and March (1984) following the study of Cohen and Frishberg (1976) involves the low-order density matrices. Using this equation, a formally exact route is laid down by means of which the exchange-correlation potential of density functional theory can be derived in terms of the third- and lower-order density matrices. An integral equation for an approximate exchange potential is obtained, which may be solved iteratively within the Slater-Kohn-Sham scheme. © 1997 John Wiley & Sons, Inc.     

A Cyclometalated IrIII Complex Conjugated to a Coumarin Derivative Is a Potent Photodynamic Agent against Prostate Differentiated and Tumorigenic Cancer Stem Cells

A cyclometalated Ir^III complex conjugated to a far-red-emitting coumarin, Ir^III-COUPY ( 3 ), was recently shown as a very promising photosensitizer suitable for photodynamic therapy of cancer. Therefore, the primary goal of this work was to deepen knowledge on the mechanism of its photoactivated antitumor action so that this information could be used to propose a new class of compounds as drug candidates for curing very hardly treatable human tumors, such as androgen resistant prostatic tumors of metastatic origin. Conventional anticancer chemotherapies exhibit several disadvantages, such as limited efficiency to target cancer stem cells (CSCs), which are considered the main reason for chemotherapy resistance, relapse, and metastasis. Herein, we show, using DU145 tumor cells, taken as the model of hormone-refractory and aggressive prostate cancer cells resistant to conventional antineoplastic drugs, that the photoactivated conjugate 3 very efficiently eliminates both prostate bulk (differentiated) and prostate hardly treatable CSCs simultaneously and with a similar efficiency. Notably, the very low toxicity of Ir^III-COUPY conjugate in the prostate DU145 cells in the dark and its pronounced selectivity for tumor cells compared with noncancerous cells could result in low side effects and reduced damage of healthy cells during the photoactivated therapy by this agent. Moreover, the experiments performed with the 3D spheroids formed from DU145 CSCs showed that conjugate 3 can penetrate the inner layers of tumor spheres, which might markedly increase its therapeutic effect. Also interestingly, this conjugate induces apoptotic cell death in prostate cancer DU145 cells associated with calcium signaling flux in these cells and autophagy. To the best of our knowledge, this is the first study demonstrating that a photoactivatable metal-based compound is an efficient agent capable of killing even hardly treatable CSCs.     

Explicit density–potential relation for 4-electron atoms in 2-orbital S states

An explicit relation is derived between the one-body potential energy and the electron density for the ground state of the Be atom in a nonrelativistic framework. This same relation applies to any four-electron atomic ion (or to Be itself) in a state where the electrons occupy two doubly filled orbitals. The relation is interpreted as an exact Hartree-like model of the Hohenberg–Kohn theorem within the general context of N electrons and a potential that is not necessarily spherically symmetrical.     

Metal-insulator transition in hydrogen and in expanded alkali metals

Two methods are considered for testing the stability of an electron gas to formation of bound states round a pair of protons. In the first, the screened potential for the two protons is set up as a superposition, which is appropriate in a very high density electron gas. The condition for bound state formation is then examined in the two-centre problem. The density thus obtained is in the right density range to accord with the experiment of Hawke et al. for producing cold metallic hydrogen.This has encouraged us to attempt a more ambitious calculation, namely the investigation of the Heitler-London energy of a model H₂ molecule with screened electron-nuclear and electron-electron interactions, the screening being again through appropriate introduction of the Thomas-Fermi screening radius. The merit of this second model is that the theory contains the Heitler-London value of the dissociation energy of the free H₂ molecule in the limit when the density of the electron gas tends to zero. This feature, the binding energy of the diatomic and its importance in distinguishing the metal-insulator transition in hydrogen from those expected to occur in expanded alkali metals is stressed. The second point we stress is that, in both the models discussed above, there is a close connection with the one-centre criterion for bound state formation. Though we have not carried out detailed two-centre calculations for expanded alkali metals, nevertheless some discussion is given of the one-centre bound state criterion in these metals.Some remarks are also made on the dielectric function of molecular crystals, in relation to the insulator-metal transition.     

Complexity and criticality in fusion, space and astrophysical plasmas

Techniques from complexity and criticality theory have fruitful applications to a wide range of natural and laboratory plasma systems. Here we review examples that have direct observational relevance, spanning fusion, the Earth's magnetosphere, the sun and astrophysical accretion disks. The complex systems techniques range from sandpiles to a novel loop-based dynamical model, together with modern approaches to model-independent data analysis.