A long-standing challenge to evolutionary theory has been whether it can explain the origin of complex organismal features. We examined this issue using digital organisms—computer programs that ...

Abstract: This paper addresses computing complex functions using unipolar stochastic logic. Stochastic computing requires simple logic gates and is inherently fault-tolerant. Thus, these structures ...

If the evolution of complex organisms were a road trip, then the simple country drives are what get you there. And sometimes even potholes along the way are important. An interdisciplinary team of ...

Real-valued functions of complex arguments violate the Cauchy-Riemann conditions and, consequently, do not have Taylor series expansion. Therefore, optimization methods based on derivatives cannot be ...

Abstract: Summary form only given. Early was proposed new types of basis functions for variational calculations of the quantum-mechanical systems with Coulomb interaction between the particles. This ...

In this effort, we present a new definition of the Steiner symmetrization by using special analytic functions in a complex domain (the open unit disk) with respect to the origin. This definition will ...

Complex analysis, the study of functions of complex variables, is traditionally a branch of pure mathematics. However, its applications in machine learning and AI are emerging in several key areas, ...

A script for generating the following examples can be found at examples.py. To use this module just place the script cplotting_tools.py in your working directory. It can be imported like this: ...

Complex integration is a branch of calculus that deals with the integration of complex-valued functions. Just as in real analysis, where we integrate real-valued functions over real intervals, in ...

Complex numbers are an extension of the more conventional real numbers that we use in everyday life. They provide a rich structure that helps with finding solutions of equations. Complex numbers are ...