Biology subjects

Stoll, E. A.

Publications and source records attributed to Stoll, E. A..

4 recordsLinked to original sources

bioRxiv2022

A thermodynamical model of non-deterministic computation in cortical neural networks

Neuronal populations in the cerebral cortex engage in probabilistic coding, effectively encoding the state of the surrounding environment with high accuracy and extraordinary energy efficiency. A new approach models the inherently probabilistic nature of cortical neuron signaling outcomes as a thermodynamic process of non-deterministic computation. A mean field approach is used, with the trial Hamiltonian maximizing free energy and minimizing the net quantity of temperature-entropy, compared with a reference Hamiltonian. Thermodynamic quantities are always conserved during the computation; free energy must be expended to produce information, and free energy is released during information compression, as correlations are identified between the encoding system and its surrounding environment. Due to the relationship between the Gibbs free energy equation and the Nernst equation, any increase in free energy is paired with a local decrease in membrane potential. As a result, this process of thermodynamic computation adjusts the likelihood of each neuron firing an action potential. This model shows that non-deterministic signaling outcomes can be achieved by noisy cortical neurons, through an energy-efficient computational process that involves optimally redistributing a Hamiltonian over some time evolution. Calculations demonstrate that the energy efficiency of the human brain is consistent with this model of non-deterministic computation, with net entropy production far too low to retain the assumptions of a classical system.

neuroscience↗

bioRxiv2022

Random electrical noise drives non-deterministic computation in cortical neural networks

In cortical neurons, spontaneous membrane potential fluctuations affect the likelihood of firing an action potential. Yet despite retaining sensitivity to random electrical noise in gating signaling outcomes, these cells achieve highly accurate computations with extraordinary energy efficiency. A new approach models the inherently probabilistic nature of cortical neuron firing as a thermodynamic process of non-deterministic computation. Typically, the cortical neuron is modeled as a binary computational unit, in either an off-state or an on-state, but here, the cortical neuron is modeled as a two-state quantum system, with some probability of switching from an off-state to an on-state. This approach explicitly takes into account the contribution of random electrical noise in gating signaling outcomes, particularly during cortical up-states. In this model, the membrane potential is described as the mixed sum of all component microstates, or the quantity of von Neumann entropy encoded by the computational unit. This distribution of macrostates is given by a density matrix, which undergoes a unitary change of basis as each unit, System A, interacts with its surrounding environment, System B. Any linear correlations reduce the number of distinguishable pure states, leading to the selection of an optimal system state in the present context. This process of information compression is shown to be equivalent to the extraction of predictive value from a thermodynamic quantity of information. Calculations demonstrate that estimated coulomb scattering profiles and decoherence timescales in cortical neurons are consistent with a quantum system, with random electrical noise driving signaling outcomes.

neuroscience↗

bioRxiv2022

The mechanics underpinning non-deterministic computation in cortical neural networks

Cortical neurons allow random electrical noise to contribute to the likelihood of firing a signal. Previous approaches have involved statistically modeling signaling outcomes in neuronal populations, or modeling the dynamical relationship between membrane potential, ion channel activation, and ion conductance in individual neurons. However, these methods do not mechanistically account for the role of random electrical noise in gating the action potential. Here, the membrane potential of a cortical neuron is modeled as the uncertainty in all component pure states, or the amount of information encoded by that computational unit. With this approach, each neuron computes the probability of transitioning from an off-state to an on-state, with the macrostate of each computational unit being a function of all component microstates. Component pure states are integrated into a physical quantity of information, and the derivative of this high-dimensional probability density yields eigenvalues, or an internally-consistent observable system state at a defined point in time. In accordance with the Hellman-Feynman theorem, the resolution of the system state is paired with a spontaneous shift in charge distribution, and so this defined system state instantly becomes the past as a new probability density emerges. This model of Hamiltonian mechanics produces testable predictions regarding the wavelength of free energy released upon information compression. Overall, this model demonstrates how cortical neurons might achieve non-deterministic signaling outcomes through noisy coincidence detection.

neuroscience↗

bioRxiv2022

Modeling electron interference at the neuronal membrane yields a holographic projection of representative information content

It has historically proven difficult to explain the relationship between neural activity and representative information content. A new approach focuses on the unique properties of cortical neurons, which allow both upstream signals and random electrical noise to affect the likelihood of reaching action potential threshold. Here, each electron is modeled as an electromagnetic point source, inter-acting in a probabilistic manner with each neuronal membrane. The electron is described as some set of probability amplitudes, distributed across five orthogonal axes: x, y, z, energy state, and time. The membrane potential of each neuron is defined by the probabilistic spatial position and atomic orbital of each local electron, after some time evolution. The mixed sum of all probabilistic component pure states is the physical quantity of information held by the neural network, given by a complex-valued wavefunction. If the probabilistic trajectory of each electron over time t affects the voltage state of multiple computational units, then the system state must be computed as a whole, with the state of each neuron being resolved as every component pure state is resolved. This computational process yields a defined system state at a defined location in time, which immediately becomes the past as a new probability density forms. If the membrane surface of each computational unit is also a charge-detecting polymer substrate that meets the criteria of a holographic recording surface, then this encoding process will generate a holographic projection of representative information content. The constructive and destructive interference of high-dimensional probability amplitudes yields a non-deterministic computational outcome for each neuron. That now-defined system state is paired with a multi-sensory percept, which is exclusively accessed by the encoding structure, with content limited by the range and sensitivity of the sensory apparatus. This model usefully offers a plausible explanation for both perceptual content and non-deterministic computational outcomes emerging from cortical neural network activity.

neuroscience↗