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The final part of the book addresses two issues: modeling of synergies and possible synergic organization of non-motor functions such as the language and the sensory function. Within the first issue, relations of synergies to the control theory is discussed with a brief overview of the central issues of the control theory such as open-loop and closed-loop control, and optimal control. Two models of synergies are described in more detail. One of them offers a neural network with back-coupling loops as the mechanism for multi-digit synergies. The other one suggests a scheme within which synergies emerge without any explicit feedback mechanisms. Further, the focus shifts to two aspects of synergies within the equilibrium-point hypothesis. One of them suggests that the principle of equilibrium-point control can by itself lead to synergies. The other deals with possible synergies in the hierarchy of control variables within the reference configuration hypothesis. The next two sections in this Part develop the notion of synergies for the sensory systems and for the production of human language. Multi-sensory interactions and synesthesia are described as possible reflections of sensory synergies. The book ends with an overview of its main points and a list of unsolved problems.

This chapter begins by describing some previously proposed models of the neuronal control of movement. These models include the λ model and the hypothesis of muscle synergies. The chapter then discusses the usefulness of higher-order sources of information about the periphery such as visual feedback and internally generated models of the body. The chapter ends with a schematic version of the cortical-spinal-muscle system and a discussion of how electrical stimulation in cortex is likely to affect this circuitry and result in complex movement.

This chapter turns to some of the tools from dynamical systems and feedback control theory that will be used in the rest of the text to analyze and design biological circuits. It first models the dynamics of a system using the input/output modeling formalism described in Chapter 1 and then studies the “robustness” of the system of a given function of the circuit. The chapter then discusses some of the underlying ideas for how to model biological oscillatory behavior, focusing on those types of oscillations that are most common in biomolecular systems. Hereafter, the chapter explores how the location of equilibrium points, their stability, their regions of attraction, and other dynamic phenomena vary based on the values of the parameters in a model. Finally, methods for reducing the complexity of the models that are introduced in this chapter are reviewed.

Inverse eigenvalue problems arise in a remarkable variety of applications. This chapter briefly highlights a few applications. The discussion is divided into six categories of applications: feedback control, applied mechanics, inverse Sturm-Liouville problem, applied physics, numerical analysis, and signal and data processing. Each category covers some additional problems.

This chapter discusses the effect of state perturbations on solutions to a hybrid system. It shows that state perturbations, of arbitrarily small size, can dramatically change the behavior of solutions. While such a phenomenon is also present in continuous-time and discrete-time dynamical systems, it is magnified in the hybrid setting, due to the flows and the jumps being constrained to the flow and the jump sets, respectively. Perturbations affecting the whole state of a hybrid system are usually considered. The resulting behaviors are quite representative of what may occur if perturbations come from state measurement error in a hybrid feedback control system or from errors present in numerical simulations of hybrid systems. The case of hybrid feedback control is given some attention in this chapter. Also, throughout the chapter, effects of perturbations are related to the regularity properties of the data of hybrid systems.

This chapter presents a framework ideally suited to an analysis of dynamic systems. Tools from control theory can be applied to elucidate the functioning of self-regulating (homeostatic) systems and to predict the effect of perturbations. It begins with an introduction to the framework of linear systems and one of the primary tools for describing their behavior: the frequency response. It then discusses how one particular type of control system, integral feedback control, plays a crucial role in both homeostasis and sensory adaptation. Next, it considers other uses of feedback mechanisms in cell signaling pathways.

This chapter outlines a view of emergent reality in which it is clear that non-physical quantities such as information and goals can have physical effect in the world of particles and forces. It explains how complexity emerges at higher levels of the hierarchy of structure on the basis of the underlying physics, leading to emergent behaviours that cannot be reduced to a description at any lower level. The first key to handling complexity is hierarchical physical structuring and function. Such functioning involves the combination of bottom-up and top-down action in the hierarchy of structure. The second key to the emergence of truly complex properties is the role of hierarchically structured information in setting goals via feedback control systems. The development of complexity in living systems requires both evolutionary processes acting over very long time periods and developmental processes acting over much shorter times.

This chapter explains feedback-dependent motor control. It presents examples that support the idea that the motor commands that move the body rely on internal predictions regarding the state of the body/environment, and sensory observations. It shows that during a movement, the motor commands depend on the state of the body part that is being controlled, as well as the overall goal of the task. This chapter suggests that the motor commands to control eye and head movements during head-free gaze changes respond to sensory feedback, and the conditions are simulated in which the head is perturbed, demonstrating how it affects the ongoing saccade of the eye.

This chapter introduces the notion of a control vector Lyapunov function as a generalization of control Lyapunov functions, showing that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector Lyapunov function. These control vector Lyapunov functions are used to develop a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel. The chapter also describes the connections between the notion of vector dissipativity and optimality of the proposed decentralized feedback control law. The proposed control framework is then used to construct decentralized controllers for large-scale nonlinear dynamical systems with robustness guarantees against full modeling uncertainty.

This chapter focuses on the mathematical design and experimental implementation of selected synthetic gene regulatory networks that embody important architectural properties. The chapter is organized as follows. Section 13.2 and 13.3 discuss the general aspects of transcriptional regulation and how transcription is modeled, respectively. The remaining sections highlight how synthetic gene regulatory systems have been designed and implemented in the bacterium Escherichia coli based on network models constructed from phenomenological mathematical descriptions of transcriptional regulation. Sections 13.4 and 13.5 discuss linear transcriptional networks and feedforward networks, respectively. Section 13.6 provides examples of networks that support bistability and oscillations by incorporating feedback control. These systems demonstrate how some of the principles investigated in Chapter 6 have been used to create living cells with complex dynamical properties.

This chapter discusses basic concepts from control theory and machine learning to facilitate a formal understanding of animal learning and motor control. It first distinguishes between feedback and feed-forward control strategies, and later introduces the classification of machine learning applications into supervised, unsupervised, and reinforcement learning problems. Next, it links these concepts with their counterparts in the domain of the psychology of animal learning, highlighting the analogies between supervised learning and classical conditioning, reinforcement learning and operant conditioning, and between unsupervised and perceptual learning. Additionally, it interprets innate and acquired actions from the standpoint of feedback vs anticipatory and adaptive control. Finally, it argues how this framework of translating knowledge between formal and biological disciplines can serve us to not only structure and advance our understanding of brain function but also enrich engineering solutions at the level of robot learning and control with insights coming from biology.

The complexities of directing complicated high-degree of freedom interactions in the Newtonian world make the human motor system the most complicated of the brain’s large-scale systems. In particular this system exhibits separate subsystems for planning, balance, and progress-monitoring, as well as vast libraries of complex movement primitives built into the spinal cord. Roughly the subsystems can be thought of as being divided into categories of fast (less than 100 milliseconds) and slow (more than 100 milliseconds). The slow subsystems are in the forebrain. The Cortex solves the formidable problem of translating the goals of a movement described in world coordinates into a posture change. This change must also include stiffness parameters, which specify how the body will react upon contacting surfaces. Posture changes are coded to reduce bandwidth, which allows them to be carried out in a timely manner by Spinal Cord circuitry, which adds essential load balancing functionality.

This chapter presents the formalisms describing discrete dynamical systems and gives an overview on the convex optimization tools and methods used to compute the analyses. A dynamical system is a typical object used in control systems or in signal processing. In some cases, it is eventually implemented in a program to perform the desired feedback control to a cyber-physical system. Language-wise, model-based languages such as LUSTRE, ANSYS SCADE, or MATLAB Simulink provide primitives to build these dynamical systems or controllers relying on simpler constructs. In terms of programs, such dynamical systems can easily be implemented as a “while true loop” initialized by the initial state and performing the update f. The simplest systems are usually directly coded in the target language, while more advanced systems are compiled through autocoders.

This chapter discusses Andy Clark’s recent explorations of Bayesian perceptual models and predictive processing. In the first part, the chapter discusses the predictive processing (PP) framework, explicating its relationship with hierarchical Bayesian models in theories of perception. In the second part, it examines the relationship between perception and action in the PP model. The overarching goal is twofold: first, to get clearer on the picture of mental activity that Clark is presenting, including what exactly is represented at the levels of the perception/action hierarchy, and the nature of the information processing it postulates; second, although the framework presented by Clark certainly has interesting novel features, some of his glosses on it are misleading. In particular, Clark’s interpretation of predictive processing as essentially a top-down, expectation-driven process, on which perception is aptly thought of as “controlled hallucination,” exaggerates the contrast with the traditional picture of perception as bottom-up and stimulus-driven. Additionally, despite the rhetoric, Clark’s PP model substantially preserves the traditional distinction between perception and action.

Last summer I took my family on a driving holiday in the American south-western desert covering many national parks. While driving along some of the long tracts of razor-straight highways, such as between Las Vegas and St George, Utah, I often fought drowsiness, not because of lack of sleep, but from the sheer monotony. A familiar experience for many, no doubt. Hardly any conscious thought is needed during such drives. It must be one’s ‘System’, as per Kahneman, which is most certainly doing what ever work is needed. Nevertheless, sleep is not an option. In spite of all the marvellous features embedded in the modern car, the ability to drive itself is, sadly, still missing. The cruise control button helps a bit, allowing one’s feet torelax as the car’s speed remains on an even keel. But the eyes and mind must remain awake and alert. When, if ever, one wonders, will cars with a ‘drive’ button become as common as those with an automatic transmission? Is driving along a perfectly straight stretch of highway really that difficult? After all, we all know that a modern jetliner can fly on autopilot, allowing even a single pilot to read a novel while ‘flying’ the aircraft on a long transcontinental flight. In fact, the jetliner would fly itself perfectly even if the pilot dozed off for many minutes or even hours. We insist that at least one pilot be awake and alert only for our own peace of mind, so as to be able to adequately respond to any emergency situation that might arise. First of all, the ubiquitous autopilot is itself quite a complex piece of equipment. Even to get a plane to fly perfectly straight along a desired heading at a fixed altitude takes a lot of work. The reason, as you must have guessed, is that nature, in the guise of the air on which our jetliner rides, can be quite unpredictable. Wind speeds and directions change continuously, even ever so slightly, requiring constant adjustments to the plane’s engine power, ailerons, flaps, and rudder. In the absence of such adjustments, our jetliner would most certainly veer off course, or lose or gain speed, even dangerously enough to trigger a powered dive or a stall.

Many of the most remarkable achievements of chemical science involve either synthesis (the design and construction of molecules) or analysis (the identification and structural characterization of molecules). We have organized our discussion of oscillating reactions along similar lines. In the previous chapter, we described how chemists have learned to build chemical oscillators. Now, we will consider how to dissect an oscillatory reaction into its component parts—the question of mechanism. A persuasive argument can be made that it was progress in unraveling the mechanism of the prototype BZ reaction in the 1970s that gave the study of chemical oscillators the scientific respectability that had been denied it since the discovery of the earliest oscillating reactions. The formulation by Field, Körös, and Noyes (Field et al., 1972) of a set of chemically and thermodynamically plausible elementary steps consistent with the observed “exotic” behavior of an acidic solution of bromate and cerium ions and malonic acid was a major breakthrough. Numerical integration (Edelson et al., 1975) of the differential equations corresponding to the FKN mechanism demonstrated beyond a doubt that chemical oscillations in a real system were consistent with, and could be explained by, the same physicochemical principles that govern "normal" chemical reactions. No special rules, no dust particles, and no vitalism need be invoked to generate oscillations in chemical reactions. All we need is an appropriate set of uni- and bimolecular steps with mass action kinetics to produce a sufficiently nonlinear set of rate equations. Just as the study of molecular structure has benefited from new experimental and theoretical developments, mechanistic studies of complex chemical reactions, including oscillating reactions, have advanced because of new techniques. Just as any structural method has its limitations (e.g., x-ray diffraction cannot achieve a resolution that is better than the wavelength of the x-rays employed), mechanistic studies, too, have their limitations. The development of a mechanism, however, has an even more fundamental and more frustrating limitation, sometimes referred to as the fundamental dogma of chemical kinetics. It is not possible to prove that a reaction mechanism is correct. We can only disprove mechanisms.

In ‘A Scandal in Bohemia’ the legendary fictional detective Sherlock Holmes deduces that his companion Watson had got very wet lately, as well as that he had ‘a most clumsy and careless servant girl’. When Watson, in amazement, asks how Holmes knows this, Holmes answers: . . . ‘It is simplicity itself . . . My eyes tell me that on the inside of your left shoe, just where the firelight strikes it, the leather is scored by six almost parallel cuts. Obviously they have been caused by someonewho has very carelessly scraped round the edges of the sole in order to remove crusted mud from it. Hence, you see, my double deduction that you had been out in vile weather, and that you had a particularly malignant boot-slitting specimen of the London slavery.’ Most of us do not share the inductive prowess of the legendary detective. Nevertheless, we all continuously look at the the world around us and, in our small way, draw inferences so as to make sense of what is going on. Even the simplest of observations, such as whether Watson’s shoe is in fact dirty, requires us to first look at his shoe. Our skill and intent drive what we look at, and look for. Those of us that may share some of Holmes’s skill look for far greater detail than the rest of us. Further, more information is better: ‘Data! Data! Data! I can’t make bricks without clay’, says Holmes in another episode. No inference is possible in the absence of input data, and, more importantly, the right data for the task at hand. How does Holmes connect the observation of ‘leather . . . scored by six almost parallel cuts’ to the cause of ‘someone . . . very carelessly scraped round the edges of the sole in order to remove crusted mud from it’? Perhaps, somewhere deep in the Holmesian brain lies a memory of a similar boot having been so damaged by another ‘specimen of the London slavery’?Or, more likely,many different ‘facts’, such as the potential causes of damage to boots, including clumsy scraping; that scraping is often prompted by boots having been dirtied by mud; that cleaning boots is usually the job of a servant; as well as the knowledge that bad weather results in mud.