Velexi consists of a team of Computational/Data Scientists, Mathematicians and Software Engineers. We leverage our experience across multiple technical fields to create elegant solutions to cutting-edge problems. Velexi provides scientific and engineering consulting services to a variety of organizations.• Perform research and prepare technical reports to support client needs. Example research areas: computational science & engineering, data science, machine learning, applied mathematics, and statistical modeling.• Design and develop custom data science, scientific and high-performance computing software solutions for clients.• Develop and maintain business and client relations.• Manage business operations.

Velexi Research (https://velexi.com/research) is dedicated to releasing and capturing the natural creativity of the human spirit and the power of serendipitous interaction of ideas. We firmly believe that the combination of creativity, sustained effort, and chance can drive innovation and discovery.• Developed Optimal Time Step (OTS) method that boosts the effective order of accuracy for finite difference schemes through careful time step selection and non-iterative defect correction.• Developed Direct Matrix Method formalization for representing discretized integro-differential equations. Benefits of the Direct Matrix Method formalization include: straightforward calculation of Jacobians for nonlinear integro-differential equations directly in matrix form and simple translation of discretized integro-differential equations into MATLAB.• Developed several open-source scientific software packages: Level Set Method Library (LSMLIB), Pseudospectral Library (PSLIB)• Researched and developed GPU computing applications.

• Managed a small private investment portfolio. My responsibilities included: investment research, trade execution, investment account maintenance, performance analysis and reporting, and tax preparation.

• Designed and developed a Python package for generating price models.• Designed and developed data processing pipeline for handling large volumes of product and price data.

• Collaborated with researchers at IHPC on phase field and crystal growth simulations

• Researched machine learning techniques for image and video recognition applications.• Developed image processing pipeline for video analytics product.• Prepared technical report highlighting state-of-the-art in image segmentation and object recognition.

• Developed mathematical models and computer simulations for dislocation dynamics based on level set methods.• Studied triply-periodic surfaces using a variational level set formulation using a combination of analytical and computational methods.• Studied surface conservation laws at microscopically diffuse interfaces using asymptotic analysis methods.

• Designed and implemented core financial engine.

* Contributed to development of the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) library.* Founded/Co-organized Math Study Group.