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Truong, Phan Minh Duc

Publications and source records attributed to Truong, Phan Minh Duc.

Conotoxin Prediction: New Features to Increase Prediction Accuracy

Conotoxins are toxic, disulfide-bond-rich peptides from cone snail venom that target a wide range of receptors and ion channels with multiple pathophysiological effects. Conotoxins have extraordinary potential for medical therapeutics that include cancer, microbial infections, epilepsy, autoimmune diseases, neurological conditions, and cardiovascular disorders. Despite the potential for these compounds in novel therapeutic treatment development, the process of identifying and characterizing the toxicities of conotoxins is difficult, costly, and time-consuming. This challenge requires a series of diverse, complex, and labor-intensive biological, toxicological, and analytical techniques for effective characterization. While recent attempts, using machine learning based solely on primary amino acid sequences to predict biological toxins (e.g., conotoxins and animal venoms), have improved toxin identification, these methods are limited due to peptide conformational flexibility and the high frequency of cysteines present in toxin sequences. This results in an enumerable set of disulfide-bridged foldamers with different conformations of the same primary amino acid sequence that affect function and toxicity levels. Consequently, a given peptide may be toxic when its cysteine residues form a particular disulfide-bond pattern, while alternative bonding patterns (isoforms) or its reduced form (free cysteines with no disulfide bridges) may have little or no toxicological effects. Similarly, the same disulfide-bond pattern may be possible for other peptide sequences and result in different conformations that all exhibit varying toxicities to the same receptor or to different receptors. We present here new features, when combined with primary sequence features to train machine learning algorithms to predict conotoxins, that significantly increase prediction accuracy.

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Challenging the Curse of Dimensionality in Multidimensional Numerical Integration by Using a Low-Rank Tensor-Train Format

Numerical integration is a basic step in the implementation of more complex numerical algorithms suitable, for example, to solve ordinary and partial differential equations. The straightforward extension of a one-dimensional integration rule to a multidimensional grid by the tensor product of the spatial directions is deemed to be practically infeasible beyond a relatively small number of dimensions, e.g., three or four. In fact, the computational burden in terms of storage and floating point operations scales exponentially with the number of dimensions. This phenomenon is known as the curse of dimensionality and motivated the development of alternative methods such as the Monte Carlo method. The tensor product approach can be very effective for high-dimensional numerical integration if we can resort to an accurate low-rank tensor-train representation of the integrand function. In this work, we discuss this approach and present numerical evidence showing that it is very competitive with the Monte Carlo method in terms of accuracy and computational costs up to several hundredths of dimensions if the integrand function is regular enough and a sufficiently accurate low-rank approximation is available.

97 MATHEMATICS AND COMPUTING↗

Factorization of Binary Matrices: Rank Relations, Uniqueness and Model Selection of Boolean Decomposition

The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantageous method to interpret and analyze data. In this work, we examine the factorizations of binary matrices using standard arithmetic (real and nonnegative) and logical operations (Boolean and $\mathbb{Z}$ 2 ). We examine the relationships between the different ranks, and discuss when factorization is unique. In particular, we characterize when a Boolean factorization X = W$\land$H has a unique W, a unique H (for a fixed W), and when both W and H are unique, given a rank constraint. We introduce a method for robust Boolean model selection, called BMFk, and show on numerical examples that BMFk not only accurately determines the correct number of Boolean latent features but reconstruct the pre-determined factors accurately.

97 MATHEMATICS AND COMPUTING↗