On Curvature in Noncommutative Geometry

A general definition of a bimodule connection in noncommutative geometry has been recently proposed. For a given algebra this definition is compared with the ordinary definition of a connection on a left module over the associated enveloping algebra. The corresponding curvatures are also compared.Comment: 16 pages, PlainTe

Linear Connections on Fuzzy Manifolds

Linear connections are introduced on a series of noncommutative geometries which have commutative limits. Quasicommutative corrections are calculated.Comment: 10 pages PlainTex; LPTHE Orsay 95/42; ESI Vienna 23

Linear connections on matrix geometries

A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique metric connection.Comment: 14p, LPTHE-ORSAY 94/9

On the first order operators in bimodules

We analyse the structure of the first order operators in bimodules introduced by A. Connes. We apply this analysis to the theory of connections on bimodules generalizing thereby several proposals.Comment: 13 pages, AMSLaTe

How Did E. M. Walker Measure the Length of the Labium of Nymphs of \u3ci\u3eAeshna\u3c/i\u3e and \u3ci\u3eRhionaeschna\u3c/i\u3e (Odonata: Aeshnidae)?

The exhaustive studies of nymphs of Aeshna Fabricius and Rhionaeschna Förster by E. M. Walker (1912-1958) have long guided the taxonomy of these groups and formed the basis for keys still in use today. However, uncertainty about how he measured the length of the labium, including the varied terminology he used over the duration of his career concerning this structure, has led to confusion about application of his taxonomic recommendations. We recalculated ratios of the maximum width/length [W(max)/L] by measuring the illustration dimensions of folded labia and prementums in publications throughout his career and compared these data with the ratios he stated in those publications and with ratios derived from measurements of specimens in our collections. Our results show that from 1912 to 1941, Walker restricted length measurement to the prementum proper (which he called the “mentum of the labium”), exclusive of the ventrally visible portion of the postmental hinge. However, in 1941 he reported ratios from length measurements done two ways, excluding the postmental hinge in his description of the nymph of A. verticalis Hagen, but including the hinge in his description of the nymph of A. septentrionalis Burmeister (Whitehouse 1941). In Walker’s most recent and influential work (1958), he included the postmental hinge in labium length measurements of nine species, but restricted length measurements to the prementum for five others. He was consistent with the use of terms, using both “folded labium” by which he meant the prementum plus the postmental hinge, and “prementum” by which he meant only that structure. However, Walker’s descriptions of the labium in his latest work are buried in long, frequently punctuated sentences that for most species include the terms “folded labium” and “prementum” in the same sentence, so careful reading is required to know which term is intended in the width/length ratio. Width/length ratios we each calculated independently were invariably similar for a given species and were usually similar to Walker’s stated ratio for that species. These similarities affirm our conclusion that while labium measurements must be done with care, they are closely repeatable among workers and will consistently lead to correct determinations in properly designed couplets of dichotomous keys to these genera. We recommend measuring the length of the prementum proper in future studies of these genera when labium ratios are calculated because we found less variability in those cases than when the measurements included the postmental hinge. An approximate conversion between the two methods of calculating W(max)/L ratios can be made as follows: ratio calculated when the length of the prementum excluding the postmental hinge is used x 0.88 is approximately equal to the ratio when the postmental hinge is included for species of Aeshna and Rhionaeschna in North America

Classical Gravity on Fuzzy Space-Time

A review is made of recent efforts to find relations between the commutation relations which define a noncommutative geometry and the gravitational field which remains as a shadow in the commutative limit.Comment: Lecture given at the 30th International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, Germany, August 27-31, 1996; 11 Pages LaTe

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.