arXiv subjects

Todd Coleman

Publications and source records attributed to Todd Coleman.

6 recordsLinked to original sources

arXiv2026

Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks

We study a network whose rich spatiotemporal dynamics have recently been shown to enable dynamics-based computation, including logic gates, short-term memory, and simple encryption. The network's time dynamics can be exactly solved through a nonlinear coordinate transformation. Here, we derive an exact analytical expression for the network's time-dependent maximum Lyapunov exponent (MLE). We demonstrate, both numerically and analytically, that the network exhibits positive MLEs during the transients that are useful for computation. Our framework enables algebraic manipulation of transient lifetimes through network connectivity and initial conditions, providing a rigorous theoretical foundation for understanding and controlling computation with transients.

nlin.CD↗

arXiv2023

An exact mathematical description of computation with transient spatiotemporal dynamics in a complex-valued neural network

We study a complex-valued neural network (cv-NN) with linear, time-delayed interactions. We report the cv-NN displays sophisticated spatiotemporal dynamics, including partially synchronized ``chimera'' states. We then use these spatiotemporal dynamics, in combination with a nonlinear readout, for computation. The cv-NN can instantiate dynamics-based logic gates, encode short-term memories, and mediate secure message passing through a combination of interactions and time delays. The computations in this system can be fully described in an exact, closed-form mathematical expression. Finally, using direct intracellular recordings of neurons in slices from neocortex, we demonstrate that computations in the cv-NN are decodable by living biological neurons. These results demonstrate that complex-valued linear systems can perform sophisticated computations, while also being exactly solvable. Taken together, these results open future avenues for design of highly adaptable, bio-hybrid computing systems that can interface seamlessly with other neural networks.

cs.NE↗

arXiv2016

Grand Challenges for Global Brain Sciences

The next grand challenges for society and science are in the brain sciences. A collection of 60+ scientists from around the world, together with 10+ observers from national, private, and foundations, spent two days together discussing the top challenges that we could solve as a global community in the next decade. We eventually settled on three challenges, spanning anatomy, physiology, and medicine. Addressing all three challenges requires novel computational infrastructure. The group proposed the advent of The International Brain Station (TIBS), to address these challenges, and launch brain sciences to the next level of understanding.

q-bio.NC↗

arXiv2011

Information-Theoretic Viewpoints on Optimal Causal Coding-Decoding Problems

In this paper we consider an interacting two-agent sequential decision-making problem consisting of a Markov source process, a causal encoder with feedback, and a causal decoder. Motivated by a desire to foster links between control and information theory, we augment the standard formulation by considering general alphabets and a cost function operating on current and previous symbols. Using dynamic programming, we provide a structural result whereby an optimal scheme exists that operates on appropriate sufficient statistics. We emphasize an example where the decoder alphabet lies in a space of beliefs on the source alphabet, and the additive cost function is a log likelihood ratio pertaining to sequential information gain. We also consider the inverse optimal control problem, where a fixed encoder/decoder pair satisfying statistical conditions is shown to be optimal for some cost function, using probabilistic matching. We provide examples of the applicability of this framework to communication with feedback, hidden Markov models and the nonlinear filter, decentralized control, brain-machine interfaces, and queuing theory.

cs.IT↗

arXiv2003

Universal light quark mass dependence and heavy-light meson spectroscopy

Clean predictions are presented for all the spin-averaged heavy-light meson spectroscopies. A new symmetry is identified wherein the energy eigenstates have a universal dependence on both the light and heavy quark masses. This universality is used in an efficient analysis of these mesons within the QCD string/flux tube picture. Unique predictions for all the D, D_s, B, and B_s type mesons in terms of just four measured quantities.

hep-ph↗

arXiv2003

QCD String Structure in Vector Confinement

We demonstrate that the Nambu-Goto string spectroscopy with massless quarks is replicated in highly excited states of the linear vector confinement potential. For deep radial excitations we observe that the Regge slope, spacing between daughter trajectories, and absolute state energies agree with those of the QCD string.

hep-ph↗