Financial conditions, alternative asset management and political risks: trying to make sense of our times.

Developments in the financial sector have led to an expansion in its ability to spread risks. The increase in the risk bearing capacity of economies, as well as in actual risk taking, has led to a range of financial transactions that hitherto were not possible, and has created much greater access to finance for firms and households. On net, this has made the world much better off. Concurrently, however, we have also seen the emergence of a whole range of intermediaries, such as hedge funds, whose incentive structures can lead them to take more risk, especially in times of plentiful liquidity and stability. As a result, under some conditions, economies may be more exposed to financial-sector-induced turmoil than in the past. I highlight concerns about the political spillovers if such instability arises.

Construction of Block Orthogonal STBCs and Reducing Their Sphere Decoding Complexity

Construction of high rate Space Time Block Codes (STBCs) with low decoding complexity has been studied widely using techniques such as sphere decoding and non Maximum-Likelihood (ML) decoders such as the QR decomposition decoder with M paths (QRDM decoder). Recently Ren et al., presented a new class of STBCs known as the block orthogonal STBCs (BOSTBCs), which could be exploited by the QRDM decoders to achieve significant decoding complexity reduction without performance loss. The block orthogonal property of the codes constructed was however only shown via simulations. In this paper, we give analytical proofs for the block orthogonal structure of various existing codes in literature including the codes constructed in the paper by Ren et al. We show that codes formed as the sum of Clifford Unitary Weight Designs (CUWDs) or Coordinate Interleaved Orthogonal Designs (CIODs) exhibit block orthogonal structure. We also provide new construction of block orthogonal codes from Cyclic Division Algebras (CDAs) and Crossed-Product Algebras (CPAs). In addition, we show how the block orthogonal property of the STBCs can be exploited to reduce the decoding complexity of a sphere decoder using a depth first search approach. Simulation results of the decoding complexity show a 30% reduction in the number of floating point operations (FLOPS) of BOSTBCs as compared to STBCs without the block orthogonal structure.Comment: 16 pages, 7 figures; Minor changes in lemmas and construction

Cross-connections of the singular transformation semigroup

Cross-connection is a construction of regular semigroups using certain categories called normal categories which are abstractions of the partially ordered sets of principal left (right) ideals of a semigroup. We describe the cross-connections in the semigroup $Sing(X)$ of all non-invertible transformations on a set $X$. The categories involved are characterized as the powerset category $\mathscr{P}(X)$ and the category of partitions $\Pi(X)$. We describe these categories and show how a permutation on $X$ gives rise to a cross-connection. Further we prove that every cross-connection between them is induced by a permutation and construct the regular semigroups that arise from the cross-connections. We show that each of the cross-connection semigroups arising this way is isomorphic to $Sing(X)$. We also describe the right reductive subsemigroups of $Sing(X)$ with the category of principal left ideals isomorphic to $\mathscr{P}(X)$. This study sheds light into the more general theory of cross-connections and also provides an alternate way of studying the structure of $Sing(X)$

Solar wind helium, neon and argon released by oxidation of metal grains from the Weston chondrite

A set of experiments were carried out to test the feasibility of determining unfractionated elemental and isotopic ratios for the noble gases in the presumably ancient solar wind present in the gas rich meteorites. The problems of diffusive loss was avoided by analyzing metal rather than the usual silicates. In order to avoid chemical, and even harsh physical, treatment of the sample, which might have affected the surfaces of metal grains, a means of analyzing the metal in the presence of residual silicate not removed by gentle crushing and magnetic separation was devised. Preliminary results given were obtained by taking advantage of the differing properties of metal and silicates with regard to diffusion. The results suggests that, with some modifications in the choice of pyrolysis and combustion temperatures and in the amount of O2 used, it should be possible, by oxidizing the surfaces of metal grains from gas rich meteorites, to obtain data on solar wind that has not been fractionated by diffusive loss