Neuronal firing patterns have significant spatiotemporal variety with no agreed upon theoretical framework. Using a combined experimental and modeling approach, we found that spike interval statistics can be described by discrete modes of activity. A "ground state" (GS) mode of low-rate spiking is universal among forebrain excitatory neurons and characterized by irregular spiking at a cell-specific rate. In contrast, "activated state" (AS) modes consist of spiking at characteristic timescales and regularity and are specific to neurons in a given region and brain state. We find that the majority of spiking is contributed by GS mode, while neurons can transiently switch to AS spiking in response to stimuli or in coordination with population activity patterns. We hypothesize that GS spiking serves to maintain a persistent backbone of neuronal activity while AS modes support communication functions.

Connectomes derived from volume EM imaging of the brain can generate detailed physical models of every neuron, and simulators such as NEURON or GENESIS are designed to work with such models. In principal, combining these technologies, plus transmitter and channel models, should allow detailed and accurate simulation of real neural circuits. Here we experiment with this combination, using a well-studied system (motion detection in Drosophila). Since simulation requires both the physical geometry (which we have) and the models of the synapses (which are not currently available), we built approximate synapses corresponding to their known and estimated function. Once we did so, we reproduced direction selectivity in T4 cells, one of the main functions of this neural circuit. This verified the basic functionality of both extraction and simulations, and provided a biologically relevant computation we could use in further experiments. We then compared models with different degrees of physical realism, from full detailed models down to models consisting of a single node, to examine the tradeoff of simulation resources required versus accuracy achieved.Our results show that much simpler models may be adequate, at least in the case of medulla neurons in Drosophila. Such models can be easily derived from fully detailed models, and result in simulations that are much smaller, much faster, and accurate enough for many purposes. Biologically, we show that a lumped neuron model reproduces the main motion detector operation, confirming the result of Gruntman [1], that dendritic compution is not required for this function.

Online decision-making can be formulated as the popular stochastic multi-armed bandit problem where a learner makes decisions (or takes actions) to maximize cumulative rewards collected from an unknown environment. A specific variant of the bandit problem is the non-stationary stochastic multiarmed bandit problem, where the reward distributions-which are unknown to the learner-change over time. This paper proposes to model non-stationary stochastic multi-armed bandits as an unknown stochastic linear dynamical system as many applications, such as bandits for dynamic pricing problems or hyperparameter selection for machine learning models, can benefit from this perspective. Following this approach, we can build a matrix representation of the system's steady-state Kalman filter that takes a set of previously collected observations from a time interval of length s to predict the next reward that will be returned for each action. This paper proposes a solution in which the parameter s is determined via an adaptive algorithm by analyzing the model uncertainty of the matrix representation. This algorithm helps the learner adaptively adjust its model size and its length of exploration based on the uncertainty of its environmental model. The effectiveness of the proposed scheme is demonstrated through extensive numerical studies, revealing that the proposed scheme is capable of increasing the rate of collected cumulative rewards.

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