I'm interested in many different research areas, especially those with an emphasis on math and creating new algorithms.
The new hashgraph consensus algorithm (illustrated with examples) allows a group to come to agreement on an ordering for transactions, and to on the outcome of running code (smart contracts). It
is Byzantine Fault Tolerant, and yields a database that is ACID compliant. Past approaches to this problem have included blockchain, leader-based systems, and voting-based systems. Hashgraph is different in that it ensures fairness of the ordering of events, and fairness in the consensus timestamps. It is more resistant to DDoS attacks than leader-based systems, more computationally efficient than proof-of-work blockchains, and more bandwidth efficient than voting-based systems. An implementation of it (with example apps) is available for download in an SDK.
Traditional jam resistant radios require some kind of secret that is shared by the sender and receiver, but unknown to the jammer. The BBC system gives equally good jam resistance, but without the shared secret. It allows ad hoc networks to establish communication without having to share a key in advance, and without worrying about an attacker capturing the key. BBC is the only known system that can provide unkeyed jam resistance against an adversary with large amounts of computational power. When combined with the new Glowworm hash function, there are both theoretical and empirical results showing the security of the system. More recent work suggests the HBT system may provide a second approach to providing unkeyed jam resistance.
The first reinforcement learning algorithms with guaranteed convergence on neural networks, as well as the ability to optimize both value and policy functions simultaneously, rather than just using dynamic programming to reduce Bellman residual error. A more detailed description of these is in the dissertation. Other research includes training neural networks to become more local (to avoid forgetting when learning new things), generating data from learned probability distributions, using neural networks for minimization, new function approximation systems for which minimization is instantaneous, and several papers on the theory of reinforcement learning, including theorems on actor-critic and value iteration systems.
Our universe has conservation laws in physics, such as conservation of energy or conservation of angular momentum. A cellular automaton defines a model of a new universe with new laws of physics, which may or may not have any such conserved quantities. New algorithms give more efficient ways to discover whether a given cellular automaton has any conserved functions, and are able to discover new conserved energy functions for many cellular automata, including where none were previously known, along with proving they don't exist in cellular automata where their existence was an open question. Furthermore, these functions can be simplified and better understood using an approach for factoring out "trivial" functions, which are functions that are conserved for all possible cellular automata. A complete theory of the trivials was developed, and used to perform such simplifications.
Computer graphics projects range from graph drawing algorithms for the Game of Sprouts, to visualizing cryptanalysis theorems for RC4, to creating jam resistant codewords that form a picture.
There are a number of fun research projects, from proving the NP-completeness of the Game of Sprouts and word hypercubes, to developing an origami fold to turn a business card into an icosahedron.
"This is My commandment, that you love one another, just as I have loved you.1 I am the good shepherd; the good shepherd lays down His life for the sheep.2 I am the way, and the truth, and the life; no one comes to the Father but through Me."3
Jesus "is the image of the invisible God, the firstborn of all creation. For by Him all things were created, both in the heavens and on earth, ... All things have been created through Him and for Him. He is before all things, and in Him all things hold together. ... For it was the Father's good pleasure for all the fullness to dwell in Him, and through Him to reconcile all things to Himself, having made peace through the blood of His cross"4