Discrete Geometry Systems, Inc.

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Company Profile

Discrete Geometry Systems, Inc. (“Discrete Geometry” or “The Company”) specializes in the research, design, and development of an advanced, state-of-the-art, computational design systems. The Company refers to this system concept as the Discrete Computational Differential Geometry Analysis (D-CDGA) System.

The D-CDGA System is a computational algebraic geometry design system. Compositionally, the portfolio is composed of a suite of state-of-the-art computational, algorithmic, and mathematical techniques, methods, principles, and concepts.

Illustrated in Figure #1, the D-CDGA System is the design of digital, discrete, and analytical surfaces. Analytical means that the surfaces conform to the concepts and principles of differential calculus. Principles of differential calculus means the surfaces are everywhere continuous, smooth, infinitely differentiable, and normalized.

Strategic Objective

Discrete Geometry’s strategic objective is to establish itself as the pre-eminent technology leader of advanced computational concepts, techniques, and algorithms for devices, software, and systems.

The Company proposes to target computational applications in mathematics, science, and engineering fields. In the sciences, targeted modeling applications include problems in computational mathematics, physics, chemistry, biophysics, molecular design, and digital communications systems and areas.

Computer-Aided Drug Design

As a market-entry strategy, Discrete Geometry proposes to develop new, cutting-edge, state-of-the-art concepts and systems of algorithms for efficiently solving large-scale problems in the market for Computer-Aided Drug Design (CADD) systems. The Company aims to develop technologies to address the global pharmaceutical and therapeutic need for the cost- and time-efficient design and discovery of new, novel, and transformative drugs.

The Company is focused on two CADD product areas:

Core Technology Overview

As the core technology, Discrete Geometry has devised a comprehensive, systematic, and generalized system of computational geometry techniques, methods, and algorithms referred to as the Discrete Computational Differential Geometry Analysis (D-CDGA) System.

As a design system, D-CDGA defines a new, innovative, advanced, and formalized system of analytical and computational geometry algorithms.

As illustrated in Figure #2, Discrete Geometry proposes to develop and market an innovative suite of computer-algebra based, computational physics and engineering systems.

As a unified system, the computational system involves, applies, and implements the same basic steps independent of:

  • Dimensionality:
    		•  the type of coordinates in the systems,
  • Complexity:
    		•  the number of variables in the systems, and
  • Contingency:
    		•  the “number of” and “type of” constraints on the systems.

Dimensionality, complexity, and contingency are all problem-specific.

Discrete & Computational Physics and Engineering Systems

(System of “Mathematical Formulations” and Algorithmic Techniques)

 

 

Figure 2: D-CDGA enables Algorithmic and Mathematical Advancements in Computational Physics and Engineering

Secondly, the D-CDGA system is an innovative application of computer algebra systems. As a computer algebra system, the D-CDGA system is the implementation of advanced applied mathematics and “symbolic processing” technology concepts.

The D-CDGA system integrates and unifies four symbolic processing areas. These symbolic processing areas are the following:

  • Symbolic Algebra:
    		•  Defines the symbolic algebraic constraints and structures of the system
  • Symbolic Geometry:
    		•  Defines the symbolic geometric surface constraints and structures of the system
  • Symbolic Differential Geometry:
    		•  Defines the symbolic partial differential equations, constraints, and structures of the system
  • Symbolic Finite Differences:
    		•  Defines the symbolic finite differences equations, constraints, and structures of the system

As a set of symbolic processing principles and concepts, the χ-Transform represents a comprehensive, systematic, integrated, coherent, and cohesive system. The symbolic processing mechanics and algorithms, of the system, enable the transformation of linear, non-linear, combinatorial, and integer optimization systems into deterministic polynomial systems.