An information theoretic method to resolve millisecond-scale spike timing precision in a comprehensive motor program

Sensory inputs in nervous systems are often encoded at the millisecond scale in a temporally precise code. There is now a growing appreciation for the prevalence of precise timing encoding in motor systems. Animals from moths to birds control motor outputs using precise spike timing, but we largely do not know at what scale timing matters in these circuits due to the difficulty of recording a complete set of spike-resolved motor signals and relatively few methods for assessing spike timing precision. We introduce a method to estimate spike timing precision in motor circuits using continuous MI estimation at increasing levels of added uniform noise. This method can assess spike timing precision at fine scales for encoding rich motor output variation. We demonstrate the advantages of this approach compared to a previously established discrete information theoretic method of assessing spike timing precision. We use this method to analyze a data set of simultaneous turning (yaw) torque output and EMG recordings from the 10 primary muscles of Manduca sexta as tethered moths visually tracked a robotic flower moving with a 1 Hz sinusoidal trajectory. We know that all 10 muscles in this motor program encode the majority of information about yaw torque in spike timings, but we do not know whether individual muscles receive information encoded at different levels of precision. Using the continuous MI method, we demonstrate that the scale of temporal precision in all motor units in this insect flight circuit is at the sub-millisecond or millisecond-scale, with variation in precision scale present between muscle types. This method can be applied broadly to estimate spike timing precision in sensory and motor circuits in both invertebrates and vertebrates.

Formation of Investment Behavior Strategy using the Game-theoretic Method

This work is aimed at developing the behavior strategy of an economic entity involved in investment activities using the game-theoretic method. To build a qualitative model, the authors considered the economic aspects of game theory and developed an algorithm for adopting the game-theoretic criteria to investment planning. The authors analyzed the investment portfolios available for business entities on the Russian market to test the model. The outcome of the article is the formation of the authors’ approach to rationalizing the behavior of an economic entity in the course of investment activities. A practical example is given in which the suggested method is used when various investment portfolios are available. The approach was tested to prove that it can be practically applied and further used in the construction of investment strategies.