A common generalization of the Fr\"olicher-Nijenhuis bracket and the Schouten bracket for symmetry multi vector fields

There is a canonical mapping from the space of sections of the bundle $\wedge T^\ast M\otimes ST\ M$ to $\Omega(T^\ast M ; T(T^\ast M))$. It is shown that this is a homomorphism on $\Omega(M;TM) for the Fr\"olicher-Nijenhuis brackets, and also on$\Gamma(ST\ M)$for the Schouten bracket of symmetric multi vector fields. But the whole image is not a subalgebra for the Fr\"olicher-Nijenhuis bracket on$\Omega(T^\ast M;T(T^\ast M))$.Comment: 14 pages, AMSTEX, LPTHE-ORSAY 94/05 and ESI 70 (1994

Risks and return of banking activities related to hedge funds.

There are approximately 10,000 hedge funds worldwide, managing assets of over USD 1.5 trillion. Investment banking activities are more and more intertwined with hedge funds, as hedge funds obtain financing from banks through prime brokerage and are clients or counterparties of banks for all sorts of products. The development of hedge funds has therefore created many opportunities for investment banks. Bank benefit from hedge funds activities directly to the extent that hedge funds are their clients. All capital market activities benefit from it, from brokerage and research to derivatives. Prime brokerage has become a growing source of income. Banks have a very important business of providing derivatives and products, from vanilla products to more complex, customized and exotic products. Hedge funds are also possible underlyings for derivatives. Many banks, including Société Générale, have developed a business of writing options on hedge funds as well as providing leverage to funds of funds. Investment banks are not only making profits by transacting with hedge funds. They also benefi t indirectly through more trading: on certain specifi c specialized market, like structured complex derivatives, there would be no market at all without the availability of hedge funds that are willing to take the risks. Together, as two intertwined partners, hedge funds and investment banks have extended the reach and effi ciency of capital markets. The benefi ts that this system brings to the economy as a whole is widely recognized. Not only do hedge funds provide important benefi ts for the economy in general but their risks are manageable. The risks for investors are overplayed. Whatever the risk measure, hedge funds are clearly less risky than equities. As regards operational risks, the market itself is able to generate protection solutions. Academic research has shown that operational risks can be dealt in the most extensive way by using managed account platforms, such as the Lyxor platform. The risks for banks are under control and the move toward “risk-based margining” has improved very much their risk management. Banks in general invest a lot of resources in monitoring hedge funds qualitatively through due-diligences. They also put different types of limits in order to cover different aspects of risks: nominal limits, stress test limits, limits on delta, limits on vega, expected tail loss limits. Moreover, they regulate their capital requirements using not only Value at Risk, the usual tool used by banks to allocate capital to market risks, but also stress tests losses based on the worst possible scenarios. These very sophisticated models are quite convincing. There is no reason to believe that they will not work in practice under stress conditions. There are also general consideration about a systemic risk that would be something else than banking risks, but it has no real argument to back it up. Hedge funds are fi rst of all the result of a signifi cant improvement of asset management techniques. These improvements are here to stay, whatever the regulatory environment will become, since these techniques will be more and more part of the mainstream asset management world. Hedge funds are more and more institutionalized. They will eventually merge with “classical” asset management, while some forms of compromises between hedge funds and classical asset management, such as absolute return funds or 130-30 funds, are becoming more common. Hedge funds are just a nice new development of capital markets that, like all past capital market developments, will be irreversible and will contribute to a more effi cient fi nancial system.

Noncommutative generalization of SU(n)-principal fiber bundles: a review

This is an extended version of a communication made at the international conference ``Noncommutative Geometry and Physics'' held at Orsay in april 2007. In this proceeding, we make a review of some noncommutative constructions connected to the ordinary fiber bundle theory. The noncommutative algebra is the endomorphism algebra of a SU(n)-vector bundle, and its differential calculus is based on its Lie algebra of derivations. It is shown that this noncommutative geometry contains some of the most important constructions introduced and used in the theory of connections on vector bundles, in particular, what is needed to introduce gauge models in physics, and it also contains naturally the essential aspects of the Higgs fields and its associated mechanics of mass generation. It permits one also to extend some previous constructions, as for instance symmetric reduction of (here noncommutative) connections. From a mathematical point of view, these geometrico-algebraic considerations highlight some new point on view, in particular we introduce a new construction of the Chern characteristic classes

Prototype ultrasonic instrument for quantitative testing

Ultrasonic instrument has been developed for use in quantitative nondestructive evaluation of material defects such as cracks, voids, inclusions, and unbonds. Instrument is provided with standard pulse source and transducer for each frequency range selected and includes integral aids that allow calibration to prescribed standards

Linear Connections in Non-Commutative Geometry

A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played by the extension to the framework of non-commutative geometry of the permutation of two copies of $\Omega^1$. The construction of the linear connection as well as the definition of torsion and curvature is first proposed in the setting of the derivations based differential calculus of Dubois- Violette and then a generalisation to the framework proposed by Connes as well as other non-commutative differential calculi is suggested. The covariant derivative obtained admits an extension to the tensor product of several copies of $\Omega^1$. These constructions are illustrated with the example of the algebra of $n \times n$ matrices.Comment: 15 pages, LMPM ../94 (uses phyzzx

Fractionalization of minimal excitations in integer quantum Hall edge channels

A theoretical study of the single electron coherence properties of Lorentzian and rectangular pulses is presented. By combining bosonization and the Floquet scattering approach, the effect of interactions on a periodic source of voltage pulses is computed exactly. When such excitations are injected into one of the channels of a system of two copropagating quantum Hall edge channels, they fractionalize into pulses whose charge and shape reflects the properties of interactions. We show that the dependence of fractionalization induced electron/hole pair production in the pulses amplitude contains clear signatures of the fractionalization of the individual excitations. We propose an experimental setup combining a source of Lorentzian pulses and an Hanbury Brown and Twiss interferometer to measure interaction induced electron/hole pair production and more generally to reconstruct single electron coherence of these excitations before and after their fractionalization.Comment: 18 pages, 10 figures, 1 tabl

Evidence Propagation and Consensus Formation in Noisy Environments

We study the effectiveness of consensus formation in multi-agent systems where there is both belief updating based on direct evidence and also belief combination between agents. In particular, we consider the scenario in which a population of agents collaborate on the best-of-n problem where the aim is to reach a consensus about which is the best (alternatively, true) state from amongst a set of states, each with a different quality value (or level of evidence). Agents' beliefs are represented within Dempster-Shafer theory by mass functions and we investigate the macro-level properties of four well-known belief combination operators for this multi-agent consensus formation problem: Dempster's rule, Yager's rule, Dubois & Prade's operator and the averaging operator. The convergence properties of the operators are considered and simulation experiments are conducted for different evidence rates and noise levels. Results show that a combination of updating on direct evidence and belief combination between agents results in better consensus to the best state than does evidence updating alone. We also find that in this framework the operators are robust to noise. Broadly, Yager's rule is shown to be the better operator under various parameter values, i.e. convergence to the best state, robustness to noise, and scalability.Comment: 13th international conference on Scalable Uncertainty Managemen