ABSTRACT
A coiled coil is a structural motif in proteins that consists of at least two α-helices wound around each other. For structural stabilization, these α-helices form interhelical contacts via their amino acid side chains. However, there are restrictions as to the distances along the amino acid sequence at which those contacts occur. As the spatial period of the α-helix is 3.6, the most frequent distances between hydrophobic contacts are 3, 4, and 7. Up to now, the multitude of possible decompositions of α-helices participating in coiled coils at these distances has not been explored systematically. Here, we present an algorithm that computes all non-redundant decompositions of sequence periods of hydrophobic amino acids into distances of 3, 4, and 7. Further, we examine which decompositions can be found in nature by analyzing the available data and taking a closer look at correlations between the properties of the coiled coil and its decomposition. We find that the availability of decompositions allowing for coiled-coil formation without putting too much strain on the α-helix geometry follows an oscillatory pattern in respect of period length. Our algorithm supplies the basis for exploring the possible decompositions of coiled coils of any period length.
Subject(s)
Computational Biology , Proteins , Amino Acid Sequence , Protein Domains , Protein Structure, Secondary , Proteins/chemistryABSTRACT
The recursive and hierarchical structure of full rooted trees is applicable to statistical models in various fields, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is not a random variable; as such, model selection to avoid overfitting is problematic. One method to solve this problem is to assume a prior distribution on the full rooted trees. This enables the optimal model selection based on Bayes decision theory. For example, by assigning a low prior probability to a complex model, the maximum a posteriori estimator prevents the selection of the complex one. Furthermore, we can average all the models weighted by their posteriors. In this paper, we propose a probability distribution on a set of full rooted trees. Its parametric representation is suitable for calculating the properties of our distribution using recursive functions, such as the mode, expectation, and posterior distribution. Although such distributions have been proposed in previous studies, they are only applicable to specific applications. Therefore, we extract their mathematically essential components and derive new generalized methods to calculate the expectation, posterior distribution, etc.
ABSTRACT
Objective:To test the relative response of a detector matrix used for measuring of the dose distribution in radiotherapy in order to ensure the accuracy and reliability of dose distribution measurement result.Methods:The two adjacent detectors can be irradiated at the same radiation dose by translating the detector matrix. The relative response of each detector to the reference detector can be obtained by combining the recursive algorithm. At the same time, the measurement data at different test steps are corrected to the reference step by setting the reference step, which correct the influence on the relative response result caused by the variation of the radiation condition and the detector response.Results:Based on the actual test of a 32 × 32 detector matrix, the relative response of each detector of the detected detector matrix to the reference detector varied from 0.896 to 1.077, with the expanded uncertainty of the relative response result being 0.8% ( k=2). Conclusions:On the premise of no known distribution of a radiation field, the relative response relationship of each detector of a detector matrix can be obtained by this method accurately and expediently, which provides a basic method for the performance evaluation of the detector matrix. The same idea can also be used to determine the relative response relationship of other detector matrices for different measurement purposes.
ABSTRACT
Suprathreshold stochastic resonance (SSR) is a distinct form of stochastic resonance, which occurs in multilevel parallel threshold arrays with no requirements on signal strength. In the generic SSR model, an optimal weighted decoding scheme shows its superiority in minimizing the mean square error (MSE). In this study, we extend the proposed optimal weighted decoding scheme to more general input characteristics by combining a Kalman filter and a least mean square (LMS) recursive algorithm, wherein the weighted coefficients can be adaptively adjusted so as to minimize the MSE without complete knowledge of input statistics. We demonstrate that the optimal weighted decoding scheme based on the Kalman-LMS recursive algorithm is able to robustly decode the outputs from the system in which SSR is observed, even for complex situations where the signal and noise vary over time.
ABSTRACT
This paper proposes a novel approach to the modelling of lumped-parameter dynamic systems, based on representing them by hierarchies of mathematical models of increasing complexity instead of a single (complex) model. Exploring the multilevel modularity that these systems typically exhibit, a general recursive modelling methodology is proposed, in order to conciliate the use of the already existing modelling techniques. The general algorithm is based on a fundamental theorem that states the conditions for computing projection operators recursively. Three procedures for these computations are discussed: orthonormalization, use of orthogonal complements and use of generalized inverses. The novel methodology is also applied for the development of a recursive algorithm based on the Udwadia-Kalaba equation, which proves to be identical to the one of a Kalman filter for estimating the state of a static process, given a sequence of noiseless measurements representing the constraints that must be satisfied by the system.
ABSTRACT
In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used.
ABSTRACT
PURPOSE: Interest in developing methods appropriate for mapping increasing amounts of genome-wide molecular data are increasing rapidly. There is also an increasing need for methods that are able to efficiently simulate such data. PATIENTS AND METHODS: In this article, we provide a graph-theory approach to find the necessary and sufficient conditions for the existence of a phylogeny matrix with k nonidentical haplotypes, n single nucleotide polymorphisms (SNPs), and a population size of m for which the minimum allele frequency of each SNP is between two specific numbers a and b. RESULTS: We introduce an O(max(n(2), nm)) algorithm for the random construction of such a phylogeny matrix. The running time of any algorithm for solving this problem would be Ω (nm). CONCLUSION: We have developed software, RAPPER, based on this algorithm, which is available at http://bioinf.cs.ipm.ir/softwares/RAPPER.
