Reward-to-risk ratios in Turkish financial markets

This paper investigates how reward-to-risk ratios compare among various government debt security (GDS) indices and sector indices in the Istanbul Stock Exchange. Risk is measured by either standard deviation or nonparametric and parametric value at risk. We find that the GDS indices have higher reward-to-risk ratios compared to the sector indices. GDS indices with longer maturities have lower reward-to-risk ratios and this reduction is especially pronounced when the ratios take downside risk into account. The reward-to-risk rankings for the sector indices are similar for each measure and the results are robust to currency conversion

Reward-to-risk ratios in Turkish financial markets (Türkiye finans piyasalarında getiri-risk rasyoları)

This paper investigates how reward-to-risk ratios compare among various government debt security (GDS) indices and sector indices in the Istanbul Stock Exchange. Risk is measured by either standard deviation or nonparametric and parametric value at risk. We find that the GDS indices have higher reward-to-risk ratios compared to the sector indices. GDS indices with longer maturities have lower reward-to-risk ratios and this reduction is especially pronounced when the ratios take downside risk into account. The reward-to-risk rankings for the sector indices are similar for each measure and the results are robust to currency conversion

Efficient networks for quantum factoring

We consider how to optimize memory use and computation time in operating a quantum computer. In particular, we estimate the number of memory quantum bits (qubits) and the number of operations required to perform factorization, using the algorithm suggested by Shor [in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society, Los Alamitos, CA, 1994), p. 124]. A K-bit number can be factored in time of order K3 using a machine capable of storing 5K+1 qubits. Evaluation of the modular exponential function (the bottleneck of Shor’s algorithm) could be achieved with about 72K3 elementary quantum gates; implementation using a linear ion trap would require about 396K3 laser pulses. A proof-of-principle demonstration of quantum factoring (factorization of 15) could be performed with only 6 trapped ions and 38 laser pulses. Though the ion trap may never be a useful computer, it will be a powerful device for exploring experimentally the properties of entangled quantum states

Efficient implementation of the Hardy-Ramanujan-Rademacher formula

We describe how the Hardy-Ramanujan-Rademacher formula can be implemented to allow the partition function $p(n)$ to be computed with softly optimal complexity $O(n^{1/2+o(1)})$ and very little overhead. A new implementation based on these techniques achieves speedups in excess of a factor 500 over previously published software and has been used by the author to calculate $p(10^{19})$, an exponent twice as large as in previously reported computations. We also investigate performance for multi-evaluation of $p(n)$, where our implementation of the Hardy-Ramanujan-Rademacher formula becomes superior to power series methods on far denser sets of indices than previous implementations. As an application, we determine over 22 billion new congruences for the partition function, extending Weaver's tabulation of 76,065 congruences.Comment: updated version containing an unconditional complexity proof; accepted for publication in LMS Journal of Computation and Mathematic

pTNoC: Probabilistically time-analyzable tree-based NoC for mixed-criticality systems

The use of networks-on-chip (NoC) in real-time safety-critical multicore systems challenges deriving tight worst-case execution time (WCET) estimates. This is due to the complexities in tightly upper-bounding the contention in the access to the NoC among running tasks. Probabilistic Timing Analysis (PTA) is a powerful approach to derive WCET estimates on relatively complex processors. However, so far it has only been tested on small multicores comprising an on-chip bus as communication means, which intrinsically does not scale to high core counts. In this paper we propose pTNoC, a new tree-based NoC design compatible with PTA requirements and delivering scalability towards medium/large core counts. pTNoC provides tight WCET estimates by means of asymmetric bandwidth guarantees for mixed-criticality systems with negligible impact on average performance. Finally, our implementation results show the reduced area and power costs of the pTNoC.The research leading to these results has received funding from the European Community’s Seventh Framework Programme [FP7/2007-2013] under the PROXIMA Project (www.proxima-project.eu), grant agreement no 611085. This work has also been partially supported by the Spanish Ministry of Science and Innovation under grant TIN2015-65316-P and the HiPEAC Network of Excellence. Mladen Slijepcevic is funded by the Obra Social Fundación la Caixa under grant Doctorado “la Caixa” - Severo Ochoa. Carles Hern´andez is jointly funded by the Spanish Ministry of Economy and Competitiveness (MINECO) and FEDER funds through grant TIN2014-60404-JIN. Jaume Abella has been partially supported by the MINECO under Ramon y Cajal postdoctoral fellowship number RYC-2013-14717.Peer ReviewedPostprint (author's final draft

GMRES-Accelerated ADMM for Quadratic Objectives

We consider the sequence acceleration problem for the alternating direction method-of-multipliers (ADMM) applied to a class of equality-constrained problems with strongly convex quadratic objectives, which frequently arise as the Newton subproblem of interior-point methods. Within this context, the ADMM update equations are linear, the iterates are confined within a Krylov subspace, and the General Minimum RESidual (GMRES) algorithm is optimal in its ability to accelerate convergence. The basic ADMM method solves a $\kappa$-conditioned problem in $O(\sqrt{\kappa})$ iterations. We give theoretical justification and numerical evidence that the GMRES-accelerated variant consistently solves the same problem in $O(\kappa^{1/4})$ iterations for an order-of-magnitude reduction in iterations, despite a worst-case bound of $O(\sqrt{\kappa})$ iterations. The method is shown to be competitive against standard preconditioned Krylov subspace methods for saddle-point problems. The method is embedded within SeDuMi, a popular open-source solver for conic optimization written in MATLAB, and used to solve many large-scale semidefinite programs with error that decreases like $O(1/k^{2})$, instead of $O(1/k)$, where $k$ is the iteration index.Comment: 31 pages, 7 figures. Accepted for publication in SIAM Journal on Optimization (SIOPT