Math, Compute, Bio🏂

The Laravel Landscape, from my point of view. Architectural Considerations Laravel isn’t just another PHP framework - it’s an architectural decision that impacts your entire development ecosystem. While it offers an elegant syntax and robust features, its true power lies in how it enables enterprise-grade applications when properly implemented. // Instead of basic routing like: Route::get('/users', [UserController::class, 'index']); // Consider domain-driven design approaches: Route::group(['domain' => '{tenant}.example.com'], function () { Route::get('/users', [TenantUserController::class, 'index']) ->middleware(['tenant.verify', 'cache.headers:public;max_age=2628000']); }); Performance Optimization The performance concerns with Laravel aren’t inherent to the framework - they’re usually symptoms of suboptimal implementation. After years of large-scale deployments, here’s what really matters: ...

PINNACLE, a novel computational model designed to enhance our understanding of protein function within specific cellular contexts. The paper presents a significant advancement in computational biology by applying geometric deep learning to address the limitation of existing models, which often overlook the contextual variability of protein functions. Below is a comprehensive review addressing key questions pertinent to evaluating research in computational biology, molecular biology, and deep learning. 1. What is the research question, and why is it important? The central question of this research is how to accurately model protein interactions in ways that account for the unique cellular and tissue environments where proteins operate. Unlike traditional models that generate a single, context-free protein representation, this study investigates the benefits of creating context-specific protein representations across various cell types. This question is of paramount importance in fields like molecular biology and therapeutic development, as proteins often display distinct functions in different cellular environments, influencing the success of therapeutic targets. By embedding protein interaction data within cell-specific contexts, this work aims to bridge a critical gap in understanding how proteins behave across different biological settings, providing valuable insights into precision medicine and the development of targeted therapies. ...

BiomedParse 1. Model Selection and Architecture BiomedParse is a transformer-based language model specifically designed for parsing biomedical text into structured representations. The key architectural choices are: Using a pre-trained BERT (Bidirectional Encoder Representations from Transformers) model as the backbone, which has shown strong performance on various natural language processing tasks. BERT is a deep bidirectional transformer that learns contextual word representations by jointly conditioning on both left and right context. ...

About I was checking some of the old communications and lectures. drop down some notes and hope will help myself some day the content below based on the senminars of Dr.Bernstein, Cancer Genomes in 3D , in Dana Farber science connect. Link The Webinar Dr. Bernstein, from Mass General Hospital, Harvard Medical School, and the Broad Institute, presented groundbreaking research on how 3D genome architecture and epigenetic modifications influence cancer development. The field has evolved significantly over the past 15 years, moving from basic genome sequencing to understanding complex epigenetic mechanisms. ...

The Fundamental Role of Gaussian Distribution in Machine Learning The Gaussian distribution, also known as the normal distribution, stands as a cornerstone in statistical modeling and machine learning. Its mathematical elegance and natural occurrence in real-world phenomena make it an indispensable tool for data scientists and researchers. Mathematical Foundation The univariate Gaussian distribution is characterized by its probability density function: $$ p(x|\mu,\sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}}\exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right) $$ ...

Higher Genus Riemann-Roch and the Geometry of Curves Riemann-Roch theorem is elegant and its proof is a cornerstone of any first course in algebraic geometry or complex analysis (for Riemann surfaces), its implications, particularly for curves of genus $g \ge 2$, continue to drive research and provide essential tools for understanding their intricate geometry. This post aims to delve into the Riemann-Roch theorem beyond the familiar low-genus cases, exploring its quantitative power and its role in unlocking deeper properties of algebraic curves. ...

Converting Integrals to Series Converting integrals to series is a powerful technique used in calculus to solve complex integration problems. This technique involves expressing an integral as an infinite series, which can then be evaluated term by term. Why Convert Integrals to Series? Converting integrals to series is useful when the integral cannot be evaluated directly. This can happen when the integral has no elementary antiderivative, or when the antiderivative is difficult to compute. By expressing the integral as a series, we can often find an approximate solution or even an exact solution in some cases. ...