Regeneration limit of classical Shannon capacity

Since Shannon derived the seminal formula for the capacity of the additive linear white Gaussian noise channel, it has commonly been interpreted as the ultimate limit of error-free information transmission rate. However, the capacity above the corresponding linear channel limit can be achieved when noise is suppressed using nonlinear elements; that is, the regenerative function not available in linear systems. Regeneration is a fundamental concept that extends from biology to optical communications. All-optical regeneration of coherent signal has attracted particular attention. Surprisingly, the quantitative impact of regeneration on the Shannon capacity has remained unstudied. Here we propose a new method of designing regenerative transmission systems with capacity that is higher than the corresponding linear channel, and illustrate it by proposing application of the Fourier transform for efficient regeneration of multilevel multidimensional signals. The regenerative Shannon limit -the upper bound of regeneration efficiency -is derived. © 2014 Macmillan Publishers Limited. All rights reserved.

VaxiJen:a server for prediction of protective antigens, tumour antigens and subunit vaccines

Background - Vaccine development in the post-genomic era often begins with the in silico screening of genome information, with the most probable protective antigens being predicted rather than requiring causative microorganisms to be grown. Despite the obvious advantages of this approach – such as speed and cost efficiency – its success remains dependent on the accuracy of antigen prediction. Most approaches use sequence alignment to identify antigens. This is problematic for several reasons. Some proteins lack obvious sequence similarity, although they may share similar structures and biological properties. The antigenicity of a sequence may be encoded in a subtle and recondite manner not amendable to direct identification by sequence alignment. The discovery of truly novel antigens will be frustrated by their lack of similarity to antigens of known provenance. To overcome the limitations of alignment-dependent methods, we propose a new alignment-free approach for antigen prediction, which is based on auto cross covariance (ACC) transformation of protein sequences into uniform vectors of principal amino acid properties. Results - Bacterial, viral and tumour protein datasets were used to derive models for prediction of whole protein antigenicity. Every set consisted of 100 known antigens and 100 non-antigens. The derived models were tested by internal leave-one-out cross-validation and external validation using test sets. An additional five training sets for each class of antigens were used to test the stability of the discrimination between antigens and non-antigens. The models performed well in both validations showing prediction accuracy of 70% to 89%. The models were implemented in a server, which we call VaxiJen. Conclusion - VaxiJen is the first server for alignment-independent prediction of protective antigens. It was developed to allow antigen classification solely based on the physicochemical properties of proteins without recourse to sequence alignment. The server can be used on its own or in combination with alignment-based prediction methods.

Predicting class II MHC-Peptide binding:a kernel based approach using similarity scores

Background - Modelling the interaction between potentially antigenic peptides and Major Histocompatibility Complex (MHC) molecules is a key step in identifying potential T-cell epitopes. For Class II MHC alleles, the binding groove is open at both ends, causing ambiguity in the positional alignment between the groove and peptide, as well as creating uncertainty as to what parts of the peptide interact with the MHC. Moreover, the antigenic peptides have variable lengths, making naive modelling methods difficult to apply. This paper introduces a kernel method that can handle variable length peptides effectively by quantifying similarities between peptide sequences and integrating these into the kernel. Results - The kernel approach presented here shows increased prediction accuracy with a significantly higher number of true positives and negatives on multiple MHC class II alleles, when testing data sets from MHCPEP [1], MCHBN [2], and MHCBench [3]. Evaluation by cross validation, when segregating binders and non-binders, produced an average of 0.824 AROC for the MHCBench data sets (up from 0.756), and an average of 0.96 AROC for multiple alleles of the MHCPEP database. Conclusion - The method improves performance over existing state-of-the-art methods of MHC class II peptide binding predictions by using a custom, knowledge-based representation of peptides. Similarity scores, in contrast to a fixed-length, pocket-specific representation of amino acids, provide a flexible and powerful way of modelling MHC binding, and can easily be applied to other dynamic sequence problems.

Identifying candidate subunit vaccines using an alignment-independent method based on principal amino acid properties

Subunit vaccine discovery is an accepted clinical priority. The empirical approach is time- and labor-consuming and can often end in failure. Rational information-driven approaches can overcome these limitations in a fast and efficient manner. However, informatics solutions require reliable algorithms for antigen identification. All known algorithms use sequence similarity to identify antigens. However, antigenicity may be encoded subtly in a sequence and may not be directly identifiable by sequence alignment. We propose a new alignment-independent method for antigen recognition based on the principal chemical properties of protein amino acid sequences. The method is tested by cross-validation on a training set of bacterial antigens and external validation on a test set of known antigens. The prediction accuracy is 83% for the cross-validation and 80% for the external test set. Our approach is accurate and robust, and provides a potent tool for the in silico discovery of medically relevant subunit vaccines.

Toward prediction of class II mouse major histocompatibility complex peptide binding affinity:in silico bioinformatic evaluation using partial least squares, a robust multivariate statistical technique

The accurate identification of T-cell epitopes remains a principal goal of bioinformatics within immunology. As the immunogenicity of peptide epitopes is dependent on their binding to major histocompatibility complex (MHC) molecules, the prediction of binding affinity is a prerequisite to the reliable prediction of epitopes. The iterative self-consistent (ISC) partial-least-squares (PLS)-based additive method is a recently developed bioinformatic approach for predicting class II peptide−MHC binding affinity. The ISC−PLS method overcomes many of the conceptual difficulties inherent in the prediction of class II peptide−MHC affinity, such as the binding of a mixed population of peptide lengths due to the open-ended class II binding site. The method has applications in both the accurate prediction of class II epitopes and the manipulation of affinity for heteroclitic and competitor peptides. The method is applied here to six class II mouse alleles (I-Ab, I-Ad, I-Ak, I-As, I-Ed, and I-Ek) and included peptides up to 25 amino acids in length. A series of regression equations highlighting the quantitative contributions of individual amino acids at each peptide position was established. The initial model for each allele exhibited only moderate predictivity. Once the set of selected peptide subsequences had converged, the final models exhibited a satisfactory predictive power. Convergence was reached between the 4th and 17th iterations, and the leave-one-out cross-validation statistical terms - q2, SEP, and NC - ranged between 0.732 and 0.925, 0.418 and 0.816, and 1 and 6, respectively. The non-cross-validated statistical terms r2 and SEE ranged between 0.98 and 0.995 and 0.089 and 0.180, respectively. The peptides used in this study are available from the AntiJen database (http://www.jenner.ac.uk/AntiJen). The PLS method is available commercially in the SYBYL molecular modeling software package. The resulting models, which can be used for accurate T-cell epitope prediction, will be made freely available online (http://www.jenner.ac.uk/MHCPred).

Modeling the peptide-T cell receptor interaction by the comparative molecular similarity indices analysis-soft independent modeling of class analogy technique

A set of 38 epitopes and 183 non-epitopes, which bind to alleles of the HLA-A3 supertype, was subjected to a combination of comparative molecular similarity indices analysis (CoMSIA) and soft independent modeling of class analogy (SIMCA). During the process of T cell recognition, T cell receptors (TCR) interact with the central section of the bound nonamer peptide; thus only positions 4−8 were considered in the study. The derived model distinguished 82% of the epitopes and 73% of the non-epitopes after cross-validation in five groups. The overall preference from the model is for polar amino acids with high electron density and the ability to form hydrogen bonds. These so-called “aggressive” amino acids are flanked by small-sized residues, which enable such residues to protrude from the binding cleft and take an active role in TCR-mediated T cell recognition. Combinations of “aggressive” and “passive” amino acids in the middle part of epitopes constitute a putative TCR binding motif

Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem

Research partially supported by INTAS grant 97-1644

Оптимизация Оценки Вероятности Ошибочной Классификации в Дискретном Случае

* Работа выполнена при поддержке РФФИ, гранты 07-01-00331-a и 08-01-00944-a

AllerTOP v.2 - a server for in silico prediction of allergens

Allergy is an overreaction by the immune system to a previously encountered, ordinarily harmless substance - typically proteins - resulting in skin rash, swelling of mucous membranes, sneezing or wheezing, or other abnormal conditions. The use of modified proteins is increasingly widespread: their presence in food, commercial products, such as washing powder, and medical therapeutics and diagnostics, makes predicting and identifying potential allergens a crucial societal issue. The prediction of allergens has been explored widely using bioinformatics, with many tools being developed in the last decade; many of these are freely available online. Here, we report a set of novel models for allergen prediction utilizing amino acid E-descriptors, auto- and cross-covariance transformation, and several machine learning methods for classification, including logistic regression (LR), decision tree (DT), naïve Bayes (NB), random forest (RF), multilayer perceptron (MLP) and k nearest neighbours (kNN). The best performing method was kNN with 85.3% accuracy at 5-fold cross-validation. The resulting model has been implemented in a revised version of the AllerTOP server (http://www.ddg-pharmfac.net/AllerTOP). © Springer-Verlag 2014.

Motzkin Decomposable Sets

Theodore Motzkin proved, in 1936, that any polyhedral convex set can be expressed as the (Minkowski) sum of a polytope and a polyhedral convex cone. We have provided several characterizations of the larger class of closed convex sets, Motzkin decomposable, in finite dimensional Euclidean spaces which are the sum of a compact convex set with a closed convex cone. These characterizations involve different types of representations of closed convex sets as the support functions, dual cones and linear systems whose relationships are also analyzed. The obtaining of information about a given closed convex set F and the parametric linear optimization problem with feasible set F from each of its different representations, including the Motzkin decomposition, is also discussed. Another result establishes that a closed convex set is Motzkin decomposable if and only if the set of extreme points of its intersection with the linear subspace orthogonal to its lineality is bounded. We characterize the class of the extended functions whose epigraphs are Motzkin decomposable sets showing, in particular, that these functions attain their global minima when they are bounded from below. Calculus of Motzkin decomposable sets and functions is provided.

Stochastic Arithmetic Theory and Experiments

Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing the efficiency of the proposed approach.

A Taxonomy of Big Data for Optimal Predictive Machine Learning and Data Mining

Big data comes in various ways, types, shapes, forms and sizes. Indeed, almost all areas of science, technology, medicine, public health, economics, business, linguistics and social science are bombarded by ever increasing flows of data begging to be analyzed efficiently and effectively. In this paper, we propose a rough idea of a possible taxonomy of big data, along with some of the most commonly used tools for handling each particular category of bigness. The dimensionality p of the input space and the sample size n are usually the main ingredients in the characterization of data bigness. The specific statistical machine learning technique used to handle a particular big data set will depend on which category it falls in within the bigness taxonomy. Large p small n data sets for instance require a different set of tools from the large n small p variety. Among other tools, we discuss Preprocessing, Standardization, Imputation, Projection, Regularization, Penalization, Compression, Reduction, Selection, Kernelization, Hybridization, Parallelization, Aggregation, Randomization, Replication, Sequentialization. Indeed, it is important to emphasize right away that the so-called no free lunch theorem applies here, in the sense that there is no universally superior method that outperforms all other methods on all categories of bigness. It is also important to stress the fact that simplicity in the sense of Ockham’s razor non-plurality principle of parsimony tends to reign supreme when it comes to massive data. We conclude with a comparison of the predictive performance of some of the most commonly used methods on a few data sets.

A Comparative Analysis of Predictive Learning Algorithms on High-Dimensional Microarray Cancer Data

This research evaluates pattern recognition techniques on a subclass of big data where the dimensionality of the input space (p) is much larger than the number of observations (n). Specifically, we evaluate massive gene expression microarray cancer data where the ratio κ is less than one. We explore the statistical and computational challenges inherent in these high dimensional low sample size (HDLSS) problems and present statistical machine learning methods used to tackle and circumvent these difficulties. Regularization and kernel algorithms were explored in this research using seven datasets where κ < 1. These techniques require special attention to tuning necessitating several extensions of cross-validation to be investigated to support better predictive performance. While no single algorithm was universally the best predictor, the regularization technique produced lower test errors in five of the seven datasets studied.

Sensor Location Problem for a Multigraph

MSC 2010: 05C50, 15A03, 15A06, 65K05, 90C08, 90C35

Multidimensional classification and diagnosis of leukemia in flow cytometry

This research is to establish new optimization methods for pattern recognition and classification of different white blood cells in actual patient data to enhance the process of diagnosis. Beckman-Coulter Corporation supplied flow cytometry data of numerous patients that are used as training sets to exploit the different physiological characteristics of the different samples provided. The methods of Support Vector Machines (SVM) and Artificial Neural Networks (ANN) were used as promising pattern classification techniques to identify different white blood cell samples and provide information to medical doctors in the form of diagnostic references for the specific disease states, leukemia. The obtained results prove that when a neural network classifier is well configured and trained with cross-validation, it can perform better than support vector classifiers alone for this type of data. Furthermore, a new unsupervised learning algorithm---Density based Adaptive Window Clustering algorithm (DAWC) was designed to process large volumes of data for finding location of high data cluster in real-time. It reduces the computational load to ∼O(N) number of computations, and thus making the algorithm more attractive and faster than current hierarchical algorithms.