Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed uncorrelated random network structure. Real gene networks typically have nontrivial topology significantly different from the random network paradigm. To address such situations, we present a general method for determining the stability of large Boolean networks of any specified network topology and predicting their steady-state behavior in response to small perturbations. Additionally, we generalize to the case where individual genes have a distribution of "expression biases," and we consider a nonsynchronous update, as well as extension of our method to non-Boolean models in which there are more than two possible gene states. We find that stability is governed by the maximum eigenvalue of a modified adjacency matrix, and we test this result by comparison with numerical simulations. We also discuss the possible application of our work to experimentally inferred gene networks.

We explore the hyperparameter space of reservoir computers used for forecasting of the chaotic Lorenz '63 attractor with Bayesian optimization. We use a new measure of reservoir performance, designed to emphasize learning the global climate of the forecasted system rather than short-term prediction. We find that optimizing over this measure more quickly excludes reservoirs that fail to reproduce the climate. The results of optimization are surprising: the optimized parameters often specify a reservoir network with very low connectivity. Inspired by this observation, we explore reservoir designs with even simpler structure, and find well-performing reservoirs that have zero spectral radius and no recurrence. These simple reservoirs provide counterexamples to widely used heuristics in the field, and may be useful for hardware implementations of reservoir computers.Reservoir computers have seen wide use in forecasting physical systems, inferring unmeasured values in systems, and classification. The construction of a reservoir computer is often reduced to a handful of tunable parameters. Choosing the best parameters for the job at hand is a difficult task. We explored this parameter space on the forecasting task with Bayesian optimization using a new measure for reservoir performance that emphasizes global climate reproduction and avoids known problems with the usual measure. We find that even reservoir computers with a very simple construction still perform well at the task of system forecasting. These simple constructions break common rules for reservoir construction and may prove easier to implement in hardware than their more complex variants while still performing as well.

. Developing a stochastic dynamic programming framework for optical tweezers based automated particle transport operations. IEEE Transactions on Automation Science and Engineering, 7(2), 218 -227, 2010. Readers are encouraged to get the official version from the journal's web site or by contacting Dr. S.K. Gupta (skgupta@umd.edu). Ashis Gopal Banerjee, Student Member, IEEE, Andrew Pomerance, Wolfgang Losert, and Satyandra K. GuptaAbstract-Automated particle transport using optical tweezers requires the use of motion planning to move the particle while avoiding collisions with randomly moving obstacles. This paper describes a stochastic dynamic programming based motion planning framework developed by modifying the discrete version of an infinite-horizon partially observable Markov decision process algorithm. Sample trajectories generated by this algorithm are presented to highlight effectiveness in crowded scenes and flexibility. The algorithm is tested using silica beads in a holographic tweezer set-up and data obtained from the physical experiments are reported to validate various aspects of the planning simulation framework. This framework is then used to evaluate the performance of the algorithm under a variety of operating conditions.Note to Practitioners-Micro and nano scale component-based devices are revolutionizing health care, energy, communication, and computing industry. Components need to be assembled together to create useful devices. Such assembly operations remain challenging in spite of the advancements in imaging, measurement, and fabrication at the small scales. This paper deals with directed assembly using optical fields that is useful for prototyping new design concepts, repairing devices, and creating templates for self-assembly.

We consider the commonly encountered situation (e.g., in weather forecast) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous system states and an imperfect model of the full system dynamics. Specifically, we attempt to utilize machine learning as the essential tool for integrating the use of past data into predictions. In order to facilitate scalability to the common scenario of interest where the spatiotemporally chaotic system is very large and complex, we propose combining two approaches: (i) a parallel machine learning prediction scheme and (ii) a hybrid technique for a composite prediction system composed of a knowledge-based component and a machine learning-based component. We demonstrate that not only can this method combining (i) and (ii) be scaled to give excellent performance for very large systems but also that the length of time series data needed to train our multiple, parallel machine learning components is dramatically less than that necessary without parallelization. Furthermore, considering cases where computational realization of the knowledge-based component does not resolve subgrid-scale processes, our scheme is able to use training data to incorporate the effect of the unresolved short-scale dynamics upon the resolved longer-scale dynamics (subgrid-scale closure).

We develop and test machine learning techniques for successfully using past state time series data and knowledge of a time-dependent system parameter to predict the evolution of the “climate” associated with the long-term behavior of a non-stationary dynamical system, where the non-stationary dynamical system is itself unknown. By the term climate, we mean the statistical properties of orbits rather than their precise trajectories in time. By the term non-stationary, we refer to systems that are, themselves, varying with time. We show that our methods perform well on test systems predicting both continuous gradual climate evolution as well as relatively sudden climate changes (which we refer to as “regime transitions”). We consider not only noiseless (i.e., deterministic) non-stationary dynamical systems, but also climate prediction for non-stationary dynamical systems subject to stochastic forcing (i.e., dynamical noise), and we develop a method for handling this latter case. The main conclusion of this paper is that machine learning has great promise as a new and highly effective approach to accomplishing data driven prediction of non-stationary systems.