Importance Sampling for Objetive Funtion Estimations in Neural Detector Traing Driven by Genetic Algorithms

To train Neural Networks (NNs) in a supervised way, estimations of an objective function must be carried out. The value of this function decreases as the training progresses and so, the number of test observations necessary for an accurate estimation has to be increased. Consequently, the training computational cost is unaffordable for very low objective function value estimations, and the use of Importance Sampling (IS) techniques becomes convenient. The study of three different objective functions is considered, which implies the proposal of estimators of the objective function using IS techniques: the Mean-Square error, the Cross Entropy error and the Misclassification error criteria. The values of these functions are estimated by IS techniques, and the results are used to train NNs by the application of Genetic Algorithms. Results for a binary detection in Gaussian noise are provided. These results show the evolution of the parameters during the training and the performances of the proposed detectors in terms of error probability and Receiver Operating Characteristics curves. At the end of the study, the obtained results justify the convenience of using IS in the training

Torus n-Point Functions for R\mathbb{R}-graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds

We consider genus one n-point functions for a vertex operator superalgebra with a real grading. We compute all n-point functions for rank one and rank two fermion vertex operator superalgebras. In the rank two fermion case, we obtain all orbifold n-point functions for a twisted module associated with a continuous automorphism generated by a Heisenberg bosonic state. The modular properties of these orbifold n-point functions are given and we describe a generalization of Fay's trisecant identity for elliptic functions.Comment: 50 page

Disorder Predictors Also Predict Backbone Dynamics for a Family of Disordered Proteins

Several algorithms have been developed that use amino acid sequences to predict whether or not a protein or a region of a protein is disordered. These algorithms make accurate predictions for disordered regions that are 30 amino acids or longer, but it is unclear whether the predictions can be directly related to the backbone dynamics of individual amino acid residues. The nuclear Overhauser effect between the amide nitrogen and hydrogen (NHNOE) provides an unambiguous measure of backbone dynamics at single residue resolution and is an excellent tool for characterizing the dynamic behavior of disordered proteins. In this report, we show that the NHNOE values for several members of a family of disordered proteins are highly correlated with the output from three popular algorithms used to predict disordered regions from amino acid sequence. This is the first test between an experimental measure of residue specific backbone dynamics and disorder predictions. The results suggest that some disorder predictors can accurately estimate the backbone dynamics of individual amino acids in a long disordered region

Disorder and residual helicity alter p53-Mdm2 binding affinity and signaling in cells

Levels of residual structure in disordered interaction domains determine in vitro binding affinities, but whether they exert similar roles in cells is not known. Here, we show that increasing residual p53 helicity results in stronger Mdm2 binding, altered p53 dynamics, impaired target gene expression and failure to induce cell cycle arrest upon DNA damage. These results establish that residual structure is an important determinant of signaling fidelity in cells