Combining Islamic Equity Portfolios and Digital Currencies: Evidence from Portfolio Diversification

Digital currencies are unregulated and potentially have a destabilizing effect coupled with increased concerns over capital gains and losses in a high volatility environment. When added to a portfolio, this currency may have certain driving factors in terms of return and risks in the case of portfolio diversification. In this study, from the Sharia angle, we follow the position of Monzer Kahf (Fatwa on Bitcoin (by Monzer Kahf). http://lightuponlight.com/blog/fatwa-on-bitcoin-by-monzer-kahf/. Accessed 03 Feb 2020, 2017) who explained that Bitcoin is considered “Like any other currency”. It should be used under the “same conditions of exchanging currencies”. Therefore, we explore the effects of adding digital currencies to an Islamic portfolio by relying on a mean-variance efficient frontier and comparing the risk-return of portfolios with and without digital currencies for different scenarios. The results show that by adding digital currencies to Shariah-compliant portfolios, its performance improves; but this depends more or less on the increase in returns than in the reduction of total risk. Specifically, digital currencies may have a big role in bringing high risks with speculative effect in portfolio diversification. Therefore, we provide some recommendations to investors and regulators to secure these currencies in Islamic capital markets

On a Tree and a Path with no Geometric Simultaneous Embedding

Two graphs $G_1=(V,E_1)$ and $G_2=(V,E_2)$ admit a geometric simultaneous embedding if there exists a set of points P and a bijection M: P -> V that induce planar straight-line embeddings both for $G_1$ and for $G_2$. While it is known that two caterpillars always admit a geometric simultaneous embedding and that two trees not always admit one, the question about a tree and a path is still open and is often regarded as the most prominent open problem in this area. We answer this question in the negative by providing a counterexample. Additionally, since the counterexample uses disjoint edge sets for the two graphs, we also negatively answer another open question, that is, whether it is possible to simultaneously embed two edge-disjoint trees. As a final result, we study the same problem when some constraints on the tree are imposed. Namely, we show that a tree of depth 2 and a path always admit a geometric simultaneous embedding. In fact, such a strong constraint is not so far from closing the gap with the instances not admitting any solution, as the tree used in our counterexample has depth 4.Comment: 42 pages, 33 figure

Visible Volume: a Robust Measure for Protein Structure Characterization

We propose a new characterization of protein structure based on the natural tetrahedral geometry of the β carbon and a new geometric measure of structural similarity, called visible volume. In our model, the side-chains are replaced by an ideal tetrahedron, the orientation of which is fixed with respect to the backbone and corresponds to the preferred rotamer directions. Visible volume is a measure of the non-occluded empty space surrounding each residue position after the side-chains have been removed. It is a robust, parameter-free, locally-computed quantity that accounts for many of the spatial constraints that are of relevance to the corresponding position in the native structure. When computing visible volume, we ignore the nature of both the residue observed at each site and the ones surrounding it. We focus instead on the space that, together, these residues could occupy. By doing so, we are able to quantify a new kind of invariance beyond the apparent variations in protein families, namely, the conservation of the physical space available at structurally equivalent positions for side-chain packing. Corresponding positions in native structures are likely to be of interest in protein structure prediction, protein design, and homology modeling. Visible volume is related to the degree of exposure of a residue position and to the actual rotamers in native proteins. In this article, we discuss the properties of this new measure, namely, its robustness with respect to both crystallographic uncertainties and naturally occurring variations in atomic coordinates, and the remarkable fact that it is essentially independent of the choice of the parameters used in calculating it. We also show how visible volume can be used to align protein structures, to identify structurally equivalent positions that are conserved in a family of proteins, and to single out positions in a protein that are likely to be of biological interest. These properties qualify visible volume as a powerful tool in a variety of applications, from the detailed analysis of protein structure to homology modeling, protein structural alignment, and the definition of better scoring functions for threading purposes.National Library of Medicine (LM05205-13

Sturmian morphisms, the braid group B_4, Christoffel words and bases of F_2

We give a presentation by generators and relations of a certain monoid generating a subgroup of index two in the group Aut(F_2) of automorphisms of the rank two free group F_2 and show that it can be realized as a monoid in the group B_4 of braids on four strings. In the second part we use Christoffel words to construct an explicit basis of F_2 lifting any given basis of the free abelian group Z^2. We further give an algorithm allowing to decide whether two elements of F_2 form a basis or not. We also show that, under suitable conditions, a basis has a unique conjugate consisting of two palindromes.Comment: 25 pages, 4 figure

Teken: pak ze voor ze jou pakken! Theorie voor gemengde leerweg: een kennismaking met de teek en de ziekte van Lyme

Dit lesmateriaal bevat de belangrijkste feiten over teken en de ziekte van Lyme en over hoe je tekenbeten kunt voorkomen (preventie). Het lesmateriaal is samengesteld door biologen van Wageningen Universiteit in het kader van het Natuurkalender programma (www.natuurkalender.nl