NishMath - #appliedmath

Researchers are actively exploring the applications of mathematics in various fields. One area of focus is the use of geometric techniques in partial differential equations (PDEs) theory. Additionally, studies are being conducted to understand the relationship between geometry and convolutional layers in neural networks.

Researchers at the Icahn School of Medicine at Mount Sinai have developed a novel computational tool, iDOMO, which leverages gene expression data to predict synergistic drug combinations for treating complex diseases. Furthermore, a new mathematical model has been created to improve the prediction of human mobility between cities, offering a valuable tool for understanding movement patterns in various contexts, potentially aiding in urban planning and disease spread prediction.


References :

• medium.com: Geometry in Neural Networks: Understanding Convolutional Layers and Its Applications

Classification:

• HashTags: #AppliedMathematics #NeuralNetworks #DrugDiscovery
• Target: ScientificProblems
• Product: AppliedMathematics
• Feature: AppliedMath
• Type: Research
• Severity: Medium

Computational simulations are advancing rapidly across various scientific domains, leveraging sophisticated techniques in applied mathematics. A new project explores implementing electromagnetic wave simulations using array languages like APL, J, or K, focusing on the Finite-Difference Time-Domain (FDTD) method. This method discretizes space into a grid, using magnetic and electric field vectors to simulate wave behavior through array arithmetic.

This method is also being applied to cosmological simulations, as evidenced by a recent publication in The Open Journal of Astrophysics titled "AI-assisted super-resolution cosmological simulations IV: An emulator for deterministic realizations" by Xiaowen Zhang, Patrick Lachance, and others. The study develops an emulator that uses deep learning to enhance low-resolution simulations with statistically correct details, producing accurate simulations and mock observations for large galaxy surveys. Additionally, research is being conducted on disaggregating log replication protocols for state machine replication, improving the efficiency and reliability of distributed data systems, as highlighted in Jack Vanlightly's analysis.


References :

• astro.theoj.org: Open Journal of Astrophysics publication on AI-assisted cosmological simulations.
• Andrew Helwer: Discussion about simulating electromagnetic waves in array languages
• Jack Vanlightly: Research on Log Replication Protocols.

Classification:

• HashTags: #Simulation #AppliedMath #Cosmology
• Target: Discovery
• Product: Simulation
• Feature: Simulation
• Type: Research
• Severity: Medium