The bisymplectomorphism group of a bounded symmetric domain

An Hermitian bounded symmetric domain in a complex vector space, given in its circled realization, is endowed with two natural symplectic forms: the flat form and the hyperbolic form. In a similar way, the ambient vector space is also endowed with two natural symplectic forms: the Fubini-Study form and the flat form. It has been shown in arXiv:math.DG/0603141 that there exists a diffeomorphism from the domain to the ambient vector space which puts in correspondence the above pair of forms. This phenomenon is called symplectic duality for Hermitian non compact symmetric spaces. In this article, we first give a different and simpler proof of this fact. Then, in order to measure the non uniqueness of this symplectic duality map, we determine the group of bisymplectomorphisms of a bounded symmetric domain, that is, the group of diffeomorphisms which preserve simultaneously the hyperbolic and the flat symplectic form. This group is the direct product of the compact Lie group of linear automorphisms with an infinite-dimensional Abelian group. This result appears as a kind of Schwarz lemma.Comment: 19 pages. Version 2: minor correction

Velocity bias in a LCDM model

We use N-body simulations to study the velocity bias of dark matter halos, the difference in the velocity fields of dark matter and halos, in a flat low- density LCDM model. The high force, 2kpc/h, and mass, 10^9Msun/h, resolution allows dark matter halos to survive in very dense environments of groups and clusters making it possible to use halos as galaxy tracers. We find that the velocity bias pvb measured as a ratio of pairwise velocities of the halos to that of the dark matter evolves with time and depends on scale. At high redshifts (z ~5) halos move generally faster than the dark matter almost on all scales: pvb(r)~1.2, r>0.5Mpc/h. At later moments the bias decreases and gets below unity on scales less than r=5Mpc/h: pvb(r)~(0.6-0.8) at z=0. We find that the evolution of the pairwise velocity bias follows and probably is defined by the spatial antibias of the dark matter halos at small scales. One-point velocity bias b_v, defined as the ratio of the rms velocities of halos and dark matter, provides a more direct measure of the difference in velocities because it is less sensitive to the spatial bias. We analyze b_v in clusters of galaxies and find that halos are ``hotter'' than the dark matter: b_v=(1.2-1.3) for r=(0.2-0.8)r_vir, where r_vir is the virial radius. At larger radii, b_v decreases and approaches unity at r=(1-2)r_vir. We argue that dynamical friction may be responsible for this small positive velocity bias b_v>1 found in the central parts of clusters. We do not find significant difference in the velocity anisotropy of halos and the dark matter. The dark matter the velocity anisotropy can be approximated as beta(x)=0.15 +2x/(x^2+4), where x is measured in units of the virial radius.Comment: 13 pages, Latex, AASTeXv5 and natbi

The variance-covariance method: Microdosimetry in time-varying low dose-rate radiation fields

The variance-covariance method is employed at low doses and in radiation fields of low dose rates from an241Am (4 nGy/s) and a90Sr (300 nGy/s) source. The preliminary applications and results illustrate some of the potential of the method, and show that the dose average of lineal energy or energy imparted can be determined over a wide range of doses and dose rates. The dose averages obtained with the variance-covariance method in time-varying fields, for which the conventional variance method is not suitable, agree well with results obtained under the condition of constant dose rate. The results are compared to data obtained in terms of the conventional single-event measurements. The method has evident advantages, such as facility and speed of measurement

Multi Agent Diagnosis: an analysis

The paper analyzes the use of a Multi Agent System for Model Based Diagnosis. In a large dynamical system, it is often infeasible or even impossible to maintain a model of the whole system. Instead, several incomplete models of the system have to be used to detect possible faults. These models may also be physically be distributed. A Multi Agent System of diagnostic agents may offer solutions for establishing a global diagnosis. If we use a separate agent for each incomplete model of the system, establishing a global diagnosis becomes a problem cooperation and negotiation between the diagnostic agents. This raises the question whether `a set of diagnostic agents, each having an incomplete model of the system, can (efficiently) determine the same global diagnosis as an ideal single diagnostic agent having the combined knowledge of the diagnostic agents?''economics of technology ;

Numerical equilibrium analysis for structured consumer resource models

In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for “Daphnia consuming algae” models in C-code. The results obtained by way of this implementation are shown in the form of graphs

^25Mg NMR study of the MgB_2 superconductor

^25Mg NMR spectra and nuclear spin-lattice relaxation time, T_1, have been measured in polycrystalline ^25MgB_2 with a superconducting transition temperature T_c = 39.0 K in zero magnetic field. From the first order and second order quadrupole perturbed NMR spectrum a quadrupole coupling frequency nu_Q = 222(1.5) kHz is obtained. T_1T = 1090(50) sK and Knight shift K_c = 242(4) ppm are temperature independent in the normal conducting phase. The ^25Mg Korringa ratio equals to 0.95 which is very close to the ideal value of unity for s-electrons. The comparison of the experimental nu_Q, T_1T, and K_c with the corresponding values obtained by LDA calculations shows an excellent agreement for all three quantities.Comment: 4 pages including 4 eps-figures, revtex

Weighted Bergman kernels and virtual Bergman kernels

We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.Comment: 12 pages. One-hour lecture for graduate students, SCV 2004, August 2004, Beijing, P.R. China. V2: typo correcte

Personal Data Protection in New Zealand: Lessons for South Africa?

In 1995 the European Union adopted a Directive on data protection. Article 25 of this Directive compels all EU member countries to adopt data protection legislation and to prevent the transfer of personal data to non-EU member countries (\'third countries\') that do not provide an adequate level of data protection. Article 25 results in the Directive having extra-territorial effect and exerting an influence in countries outside the EU. Like South Africa, New Zealand is a \'third\' country in terms of the EU Directive on data protection. New Zealand recognised the need for data protection and adopted a data protection Act over 15 years ago. The focus of this article is on the data protection provisions in New Zealand law with a view to establishing whether South Africa can learn any lessons from them. In general, it can be said that although New Zealand law does not expressly recognise a right to privacy, it has a data protection regime that functions well and that goes a long way to providing adequate data protection as required by the EU Directive on data protection. Nevertheless, the EU has not made a finding to that effect as yet. The New Zealand data protection act requires a couple of amendments before New Zealand might be adjudged ‘adequate'. South Africa's protection of the right to privacy and identity is better developed and more extensive than that of New Zealand. Privacy is recognised and protected in the law of delict and by the South African Constitution. Despite South Africa's apparently high regard for the individual's right to privacy and identity and our well-developed common and constitutional law of privacy, South Africa does not meet the adequacy requirement of the EU Directive, because we do not have a data protection Act. This means that South African participants in the information technology arena are at a constant disadvantage. It is argued that South Africa should follow New Zealand's example and adopt a data protection law as soon as possible. PER/PELJ Vol. 4 2008: pp. 61-10