Softmax is a mathematical function commonly used in machine learning, particularly in the context of classification problems. It transforms a vector of raw scores, often called logits, from a model into a vector of probabilities that sum to one. The probabilities generated by the softmax function represent the likelihood of each class being the correct classification. $$\sigma(\mathbf{z})_i = \frac{e^{z_i}}{\sum_{j=1}^K e^{z_j}}$$

Support Vector Machine (SVM) is a supervised learning algorithm used for classification and regression. It finds the best hyperplane that separates the data into different classes with the largest possible margin. SVM can work well with high-dimensional data and use different kernel functions to transform data for better separation when it is not linearly separable.$$f(x) = sign(w^T x + b)$$

Random Forest is an ensemble machine learning algorithm that builds multiple decision trees during training and merges their outputs to improve accuracy and reduce overfitting. It is commonly used for both classification and regression tasks. By averaging the predictions of several decision trees, Random Forest reduces the variance and increases model robustness, making it less prone to errors from noisy data. $$\text{Entropy}_{\text{after}} = \frac{|S_l|}{|S|}\text{Entropy}(S_l) + \frac{|S_r|}{|S|}\text{Entropy}(S_r)$$

DLVO theory is named after Derjaguin, Landau, Verwey, and Overbeek, who developed it in the 1940s. It describes the forces between charged surfaces interacting through a liquid medium. The theory combines two main types of forces

Kernel Density Estimation (KDE) is a non-parametric method to estimate the probability density function (PDF) of a random variable based on a finite set of data points. Unlike parametric methods, which assume that the underlying data follows a specific distribution (like normal, exponential, etc.), KDE makes no such assumptions and can model more complex data distributions.$$ \hat{f}(x) = \frac{1}{n \cdot h} \sum_{i=1}^{n} K\left(\frac{x - x_i}{h}\right) $$

The Taylor Series is a mathematical tool that approximates complex functions with polynomials, playing a crucial role in machine learning optimization. It enhances gradient descent by incorporating second-order information, leading to faster and more stable convergence. Additionally, it aids in linearizing non-linear models and informs regularization techniques. This post explores the significance of the Taylor Series in improving model training efficiency and understanding model behavior. $$\cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n)!} x^{2n}$$

The FoldX Suite builds on the strong fundament of advanced protein design features, already implemented in the successful FoldX3, and exploits the power of fragment libraries, by integrating in silico digested backbone protein fragments of different lengths. Such fragment-based strategy allows for new powerful capabilities: loop reconstruction, implemented in LoopX and peptide docking, implemented in PepX. The Suite also features an improved usability, thanks to a new boost Command Line Interface.

Nanopre and PacBio based Genome Assembly

Hi-C experiments explore the 3D structure of the genome, generating terabases of data to create high-resolution contact maps. Here, we introduce Juicer, an open-source tool for analyzing terabase-scale Hi-C datasets. Juicer allows users without a computational background to transform raw sequence data into normalized contact maps with one click. Juicer produces a hic file containing compressed contact matrices at many resolutions, facilitating visualization and analysis at multiple scales. Structural features, such as loops and domains, are automatically annotated.

NextDenovo is a string graph-based de novo assembler for long reads (CLR, HiFi and ONT). It uses a “correct-then-assemble” strategy similar to canu (no correction step for PacBio HiFi reads), but requires significantly less computing resources and storages. After assembly, the per-base accuracy is about 98-99.8%, to further improve single base accuracy, try NextPolish.

IgCaller is a python program designed to fully characterize the immunoglobulin gene rearrangements and oncogenic translocations in lymphoid neoplasms. It was originally developed to work with WGS data but it has been extended to work with WES and high-coverage, capture-based NGS data.

MUMmer is a system for rapidly aligning entire genomes. The current version (release 4.x) can find all 20 base pair maximal exact matches between two bacterial genomes of ~5 million base pairs each in 20 seconds, using 90 MB of memory, on a typical 1.8 GHz Linux desktop computer.

Whole Genome Sequencing (WGS) provides a deep insight into the DNA sequence of humans, animals, plants, and microbial genomes, with data analysis at the individual or population level. SNP/INDEL/CNV/SV and other variants of the genome can be fully analysed. Our sequencing analysis enables the identif wication of somatic and germline mutations as well as customized patterns of cancers and other diseases. (Novogene)

Simulated Annealing (SA) is a probabilistic technique used for finding an approximate solution to an optimization problem. It is particularly useful for problems where the search space is large and complex, and other methods might get stuck in local optima.

AI Tools for Protein Structures