# TURING Algorithms for Computation with Finite Dynamical Systems

### SDDS

SDDS module simulates the average trajectory for each variable out of numberofSimulations trajectories deterministically or stochastically

### SDDS Control

This module computes an optimal policy for a stochatic controllable system. The output will be an input for the SDDS module for simulation. Then the SDDS module will generate two trajectories: one without control and another with the control policy. The control policy is given as binary vectors where a "0" entry means no control and an entry of "1" means control. For instance, if there are 2 control nodes and 3 control edges, then a control action is a binary vector of size 5, e.g. (0,1,0,1,1), (1,1,0,0,1), etc.

### Cyclone

Calculate Dynamics of a discrete dynamical system using exhaustive search

### BasicRevEng

A method to reverse engineer gene regulatory networks from experimental data. The modeling framework used is time-discrete deterministic dynamical systems, with a finite set of states for each of the variables. The simplest examples of such models are Boolean networks, in which variables have only two possible states. The use of a larger number of possible states allows a finer discretization of experimental data and more than one possible mode of action for the variables, depending on threshold values. Furthermore, with a suitable choice of state set, one can employ powerful tools from computational algebra, that underlie the reverse-engineering algorithm, avoiding costly enumeration strategies. To perform well, the algorithm requires wildtype together with perturbation time courses. This makes it suitable for small to meso-scale networks rather than networks on a genome-wide scale. An analysis of the complexity of the algorithm is performed. The algorithm is validated on a recently published Boolean network model of segment polarity development in Drosophila melanogaster.

### Discretize

An increasing number of algorithms for biochemical network inference from experimental data require discrete data as input. For example, dynamic Bayesian network methods and methods that use the framework of finite dynamical systems, such as Boolean networks, all take discrete input. Experimental data, however, are typically continuous and represented by computer floating point numbers. The translation from continuous to discrete data is crucial in preserving the variable dependencies and thus has a significant impact on the performance of the network inference algorithms. We compare the performance of two such algorithms that use discrete data using several different discretization algorithms. One of the inference methods uses a dynamic Bayesian network framework, the other—a time‐and state‐discrete dynamical system framework. The discretization algorithms are quantile, interval discretization, and a new algorithm introduced in this article, SSD. SSD is especially designed for short time series data and is capable of determining the optimal number of discretization states. The experiments show that both inference methods perform better with SSD than with the other methods. In addition, SSD is demonstrated to preserve the dynamic features of the time series, as well as to be robust to noise in the experimental data.

### BN Reduction

BNReduction reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for large Boolean networks with high average connectivity remains an open problem

### Gfan

Gfan Reverse Engineering Method