Global analysis of dynamical decision-making models through local computation around the hidden saddle

Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity. © 2012 Trotta et al.

Decision making at the front end of innovation: The hidden influence of knowledge and decision criteria

Decision making at the front end of innovation is critical for the success of companies. This paper presents a method, called decision making based on knowledge (DeBK), which was created to analyze the decision-making process at the front end. The method evaluates the knowledge of project information and the importance of decision criteria, compiling a measure that indicates whether decisions are founded on available knowledge and what criteria are in fact being considered to delineate them. The potential contribution of DeBK is corroborated through two projects that faced decision-making issues at the front end of innovation. © 2014 RADMA and John Wiley & Sons Ltd.

Delayed-decision making in noisy bistable switches

Bistable switches are frequently encountered in biological systems. Typically, a bistable switch models a binary decision where each decision corresponds to one of the two stable equilibria. Recently, we showed that the global decision-making process in bistable switches strongly depends on a particular equilibrium point of these systems, their saddle point. In particular, we showed that a saddle point with a time-scale separation between its attractive and repulsive directions can delay the decision-making process. In this paper, we study the effects of white Gaussian noise on this mechanism of delayed decision-making induced by the saddle point. Results show that the mean decision-time strongly depends on the balance between the initial distance to the separatrix and the noise strength. © IFAC.

The Silent Period of Evidence Integration in Fast Decision Making

In a typical experiment on decision making, one out of two possible stimuli is displayed and observers decide which one was presented. Recently, Stanford and colleagues (2010) introduced a new variant of this classical one-stimulus presentation paradigm to investigate the speed of decision making. They found evidence for "perceptual decision making in less than 30 ms". Here, we extended this one-stimulus compelled-response paradigm to a two-stimulus compelled-response paradigm in which a vernier was followed immediately by a second vernier with opposite offset direction. The two verniers and their offsets fuse. Only one vernier is perceived. When observers are asked to indicate the offset direction of the fused vernier, the offset of the second vernier dominates perception. Even for long vernier durations, the second vernier dominates decisions indicating that decision making can take substantial time. In accordance with previous studies, we suggest that our results are best explained with a two-stage model of decision making where a leaky evidence integration stage precedes a race-to-threshold process. © 2013 Rüter et al.

Sequential decision making in general state space models

Many problems in control and signal processing can be formulated as sequential decision problems for general state space models. However, except for some simple models one cannot obtain analytical solutions and has to resort to approximation. In this thesis, we have investigated problems where Sequential Monte Carlo (SMC) methods can be combined with a gradient based search to provide solutions to online optimisation problems. We summarise the main contributions of the thesis as follows. Chapter 4 focuses on solving the sensor scheduling problem when cast as a controlled Hidden Markov Model. We consider the case in which the state, observation and action spaces are continuous. This general case is important as it is the natural framework for many applications. In sensor scheduling, our aim is to minimise the variance of the estimation error of the hidden state with respect to the action sequence. We present a novel SMC method that uses a stochastic gradient algorithm to find optimal actions. This is in contrast to existing works in the literature that only solve approximations to the original problem. In Chapter 5 we presented how an SMC can be used to solve a risk sensitive control problem. We adopt the use of the Feynman-Kac representation of a controlled Markov chain flow and exploit the properties of the logarithmic Lyapunov exponent, which lead to a policy gradient solution for the parameterised problem. The resulting SMC algorithm follows a similar structure with the Recursive Maximum Likelihood(RML) algorithm for online parameter estimation. In Chapters 6, 7 and 8, dynamic Graphical models were combined with with state space models for the purpose of online decentralised inference. We have concentrated more on the distributed parameter estimation problem using two Maximum Likelihood techniques, namely Recursive Maximum Likelihood (RML) and Expectation Maximization (EM). The resulting algorithms can be interpreted as an extension of the Belief Propagation (BP) algorithm to compute likelihood gradients. In order to design an SMC algorithm, in Chapter 8 uses a nonparametric approximations for Belief Propagation. The algorithms were successfully applied to solve the sensor localisation problem for sensor networks of small and medium size.