A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model

We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to what can be considered to be the most crucial nonlinear parameter, the critical time $t_c$ defined as the end of the bubble and the most probably time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings

Designing small multiple-target artificial RNAs

MicroRNAs (miRNAs) are naturally occurring small RNAs that regulate the expression of several genes. MiRNAs’ targeting rules are based on sequence complementarity between their mature products and targeted genes’ mRNAs. Based on our present understanding of those rules, we developed an algorithm to design artificial miRNAs to target simultaneously a set of predetermined genes. To validate in silico our algorithm, we tested different sets of genes known to be targeted by a single miRNA. The algorithm finds the seed of the corresponding miRNA among the solutions, which also include the seeds of new artificial miRNA sequences potentially capable of targeting these genes as well. We also validated the functionality of some artificial miRNAs designed to target simultaneously members of the E2F family. These artificial miRNAs reproduced the effects of E2Fs inhibition in both normal human fibroblasts and prostate cancer cells where they inhibited cell proliferation and induced cellular senescence. We conclude that the current miRNA targeting rules based on the seed sequence work to design multiple-target artificial miRNAs. This approach may find applications in both research and therapeutics

Generation, Comparison, and Merging of Pathways between Protein Conformations: Gating in K-Channels

We present a general framework for the generation, alignment, comparison, and hybridization of motion pathways between two known protein conformations. The framework, which is rooted in probabilistic motion-planning techniques in robotics, allows for the efficient generation of collision-free motion pathways, while considering a wide range of degrees of freedom involved in the motion. Within the framework, we provide the means to hybridize pathways, thus producing, the motion pathway of the lowest energy barrier out of the many pathways proposed by our algorithm. This method for comparing and hybridizing pathways is modular, and may be used within the context of molecular dynamics and Monte Carlo simulations. The framework was implemented within the Rosetta software suite, where the protein is represented in atomic detail. The K-channels switch between open and closed conformations, and we used the overall framework to investigate this transition. Our analysis suggests that channel-opening may follow a three-phase pathway. First, the channel unlocks itself from the closed state; second, it opens; and third, it locks itself in the open conformation. A movie that depicts the proposed pathway is available in the Supplementary Material (Movie S1) and at http://www.cs.tau.ac.il/∼angela/SuppKcsA.html