We study the orientation and speed tuning properties of spatiotemporal three-dimensional (3D) Gabor and motion energy filters as models of time-dependent receptive fields of simple and complex cells in the primary visual cortex (V1). We augment the motion energy operator with surround suppression to model the inhibitory effect of stimuli outside the classical receptive field. We show that spatiotemporal integration and surround suppression lead to substantial noise reduction. We propose an effective and straightforward motion detection computation that uses the population code of a set of motion energy filters tuned to different velocities. We also show that surround inhibition leads to suppression of texture and thus improves the visibility of object contours and facilitates figure/ground segregation and the detection and recognition of objects.

We consider arbitrarily large networks of pulse-coupled oscillators with nonzero delay where the coupling is given by the Mirollo-Strogatz function. We prove that such systems have unstable attractors (saddle periodic orbits whose stable set has non-empty interior) in an open parameter region for three or more oscillators. The evolution operator of the system can be discontinuous and we propose an improved model with continuous evolution operator.

We consider networks of pulse coupled linear oscillators with non-zero delay where the coupling between the oscillators is given by the Mirollo-Strogatz function. We prove the existence of heteroclinic cycles between unstable attractors for a network of four oscillators and for an open set of parameter values.

Periodic Double Auctions (PDAs) are commonly used in the real world for trading, e.g. in stock markets to determine stock opening prices, and energy markets to trade energy in order to balance net demand in smart grids, involving trillions of dollars in the process. A bidder, participating in such PDAs, has to plan for bids in the current auction as well as for the future auctions, which highlights the necessity of good bidding strategies. In this paper, we perform an equilibrium analysis of single unit single-shot double auctions with a certain clearing price and payment rule, which we refer to as ACPR, and find it intractable to analyze as number of participating agents increase. We further derive the best response for a bidder with complete information in a single-shot double auction with ACPR. Leveraging the theory developed for single-shot double auction and taking the PowerTAC wholesale market PDA as our testbed, we proceed by modeling the PDA of PowerTAC as an MDP. We propose a novel bidding strategy, namely MDPLCPBS. We empirically show that MDPLCPBS follows the equilibrium strategy for double auctions that we previously analyze. In addition, we benchmark our strategy against the baseline and the state-of-the-art bidding strategies for the PowerTAC wholesale market PDAs, and show that MDPLCPBS outperforms most of them consistently.

A smart grid is an efficient and sustainable energy system that integrates diverse generation entities, distributed storage capacity, and smart appliances and buildings. A smart grid brings new kinds of participants in the energy market served by it, whose effect on the grid can only be determined through high fidelity simulations. Power TAC offers one such simulation platform using real-world weather data and complex state-of-the-art customer models. In Power TAC, autonomous energy brokers compete to make profits across tariff, wholesale and balancing markets while maintaining the stability of the grid. In this paper, we design an autonomous broker VidyutVanika, the runner-up in the 2018 Power TAC competition. VidyutVanika relies on reinforcement learning (RL) in the tariff market and dynamic programming in the wholesale market to solve modified versions of known Markov Decision Process (MDP) formulations in the respective markets. The novelty lies in defining the reward functions for MDPs, solving these MDPs, and the application of these solutions to real actions in the market. Unlike previous participating agents, VidyutVanika uses a neural network to predict the energy consumption of various customers using weather data. We use several heuristic ideas to bridge the gap between the restricted action spaces of the MDPs and the much more extensive action space available to VidyutVanika. These heuristics allow VidyutVanika to convert near-optimal fixed tariffs to time-of-use tariffs aimed at mitigating transmission capacity fees, spread out its orders across several auctions in the wholesale market to procure energy at a lower price, more accurately estimate parameters required for implementing the MDP solution in the wholesale market, and account for wholesale procurement costs while optimizing tariffs. We use Power TAC 2018 tournament data and controlled experiments to analyze the performance of VidyutVanika, and illustrate the efficacy of the above strategies.