The importance of the Stability Problem in neurocomputing is discussed, as well as the need for the study of infinite networks. Stability must be the key ingredient in the solution of a problem by a neural network without external intervention. Infinite discrete networks seem to be the proper objects of study for a theory of neural computability which aims at characterizing problems solvable, in principle, by a neural network. Precise definitions of such problems and their solutions (...) are given. Some consequences are explored, in particular, the neural unsolvability of the Stability Problem for neural networks. (shrink)

Lynch et al. (Biol Philos 34:62, 2019) employ stability, specificity, and proportionality as criteria for evaluating microbiome causal explanations. Although these causal characteristics signify relevant differences between causal roles, I suggest that they should not be used as general criteria for strong or good causal explanations.

Özkal-Sanver (Theory Decis 59:193–205, 2005) studies stability and efficiency of partitions of agents in two-sided matching markets in which agents can form partitions by individual moves only, and a matching rule determines the matching in each coalition in a partition. In this study, we present the relationship between stability and efficiency of partitions that is analyzed for several matching rules and under various membership property rights codes, now allowing coalitional moves.

We define two versions of stability and efficiency of partitions and analyze their relationships for some matching rules. The stability and efficiency of a partition depends on the matching rule φ. The results are stated under various membership property rights axioms. It is shown that in a world where agents can freely exit from and enter coalitions, whenever the matching rule is individually rational and Pareto optimal, the set of φ-stable and φ-efficient partitions coincide and it is unique: (...) the grand coalition. Then we define a weaker version of stability and efficiency, namely specific to a given preference profile and find some negative results for stable matching rules. (shrink)

In this chapter I investigate the kinds of changes that psychiatric kinds undergo when they become explanatory targets of areas of sciences that are not “mature” and are in the early stages of discovering mechanisms. The two areas of science that are the targets of my analysis are cognitive neuroscience and cognitive neurobiology.

Why is space 3-dimensional? The fi rst answer to this question, entirely based on Physics, was given by Ehrenfest, in 1917, who showed that the stability requirement for n-dimensional two-body planetary system very strongly constrains space dimensionality, favouring 3-d. This kind of approach will be generically called "stability postulate" throughout this paper and was shown by Tangherlini, in 1963, to be still valid in the framework of general relativity as well as for quantum mechanical hydrogen atom, giving the (...) same constraint for space{dimensionality. In the present work, before criticizing this methodology, a brief discussion has been introduced, aimed at stressing and clarifying some general physical aspects of the problem of how to determine the number of space dimensions. Then, the epistemological consequences of Ehrenfest's methodology are critically reviewed. An alternative procedure to get at the proper number of dimensions, in which the stability postulate - and the implicit singularities in three-dimensional physics - are not an essential part of the argument, is proposed. In this way, the main epistemological problems contained in Ehrenfest's original idea are avoided. The alternative methodology proposed in this paper is realized by obtaining and discussing the n-dimensional quantum theory as expressed in Planck's law, de Broglie relation and the Heisenberg uncertainty relation. As a consequence, it is possible to propose an experiment, based on thermal neutron di raction by crystals, to directly measure space dimensionality. Finally the distinguished role of Maxwell's electromagnetic theory in the determination of space dimensionality is stressed. (shrink)

In this paper, the stabilization problem of nonholonomic chained-form systems is addressed with uncertain constants. In this paper, the active disturbance rejection control is designed to solve this problem. The proposed control strategy combines extended state observer and adaptive sliding mode controller. The control of nonholonomic chained-form systems with dynamic nonlinear uncertain terms and uncertain constants is first discussed in this paper. In comparison with existing methods, the proposed method in this paper has better performance. It is proved (...) that, with the application of the proposed control strategy, semiglobal finite-time stabilization of the systems is achieved. An example is given to illustrate the effectiveness of the proposed method. (shrink)

I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: Einstein’s static universe and Eddington’s demonstration of its instability, and the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical (...) systems theory and its epistemology. This reveals, for example, an insistence on stability as an extreme position in relation to the spectrum of physical systems which exhibit degrees of stability and fragility, one which has a pragmatic rationale, but not any deeper one. (shrink)

In this paper we consider one-to-many matching problems where the preferences of the agents involved are represented by monetary reward functions. We characterize Pareto optimal matchings by means of contractual exchange stability and matchings of maximum total reward by means of compensational exchange stability. To conclude, we show that in going from an initial matching to a matching of maximum total reward, one can always provide a compensation schedule that will be ex-post stable in the sense that there (...) will be no subset of agents who can all by deviation obtain a higher reward. The proof of this result uses the fact that the core of an associated compensation matching game with constraints is nonempty. (shrink)

Rawls addresses the problem of the stability of his conception of justice by arguing that it could become the focus of an “overlapping consensus,” in which individuals with diverse moral, philosophical, and religious views all accept the Rawlsian conception for different reasons. Using the example of Christian fundamentalists, I show that, subject to constraints that Rawls himself delineates, no such consensus is possible.

It is argued that the Nash bargaining solution cannot serve as a principle of distributive justice because (i) it cannot secure stable cooperation in repeated interactions and (ii) it cannot capture our moral intuitions concerning distributive questions. In this article, I propose a solution to the first problem by amending the Nash bargaining solution so that it can maintain stable cooperation among rational bargainers. I call the resulting principle the stabilized Nash bargaining solution. The principle defends justice in the (...) form 'each according to her basic needs and above this level according to her relative bargaining power'. In response to the second problem, I argue that the stabilized Nash bargaining solution can serve as a principle of distributive justice in certain situations where moral reasoning is reduced to instrumental reasoning. In particular, I argue that rational individuals would choose the stabilized Nash bargaining solution in Rawls' original position. (shrink)

The problem of stability in population dynamics concerns many domains of application in demography, biology, mechanics and mathematics. The problem is highly generic and independent of the population considered (human, animals, molecules,…). We give in this paper some examples of population dynamics concerning nucleic acids interacting through direct nucleic binding with small or cyclic RNAs acting on mRNAs or tRNAs as translation factors or through protein complexes expressed by genes and linked to DNA as transcription factors. The (...) networks made of these interactions between nucleic acids (considered respectively as edges and nodes of their interaction graph) are complex, but exhibit simple emergent asymptotic behaviours, when time tends to infinity, called attractors. We show that the quantity called attractor entropy plays a crucial role in the study of the stability and robustness of such genetic networks. (shrink)

We explore the computational complexity of justification, stability and relevance in incomplete argumentation frameworks (IAFs). IAFs are abstract argumentation frameworks that encode qualitative uncertainty by distinguishing between certain and uncertain arguments and attacks. These IAFs can be completed by deciding for each uncertain argument or attack whether it is present or absent. Such a completion is an abstract argumentation framework, for which it can be decided which arguments are acceptable under a given semantics. The justification status of an argument (...) in a completion then expresses whether the argument is accepted (in), not accepted because it is attacked by an accepted argument (out) or neither (undec). For a given IAF and certain argument, the justification status of that argument need not be the same in all completions. This is the issue of stability, where an argument is stable if its justification status is the same in all completions. For arguments that are not stable in an IAF, the relevance problem is of interest: which uncertain arguments or attacks should be investigated for the argument to become stable? In this paper, we define justification, stability and relevance for IAFs and provide a complexity analysis for these problems under grounded, complete, preferred and stable semantics. (shrink)

According to a widespread interpretation of John Rawls’s Liberal Principle of Legitimacy, political legitimacy requires justifiability to all reasonable citizens, but not to the unreasonable. A highly influential attempt at justifying this exclusion of the unreasonable – one first formulated by Jonathan Quong, and later endorsed by many others – is to appeal to the project of solving the problem of inherent stability. Since this is a problem that arises in a just and well-ordered society, and such (...) a society is populated by reasonable citizens only, it is only these citizens, so the reasoning goes, that are relevant for questions of legitimacy. In this paper, I show that this justification of the exclusion of the unreasonable depends on an implicitly assumed connection between stability and legitimacy. We have good reasons, I argue, to doubt that there is this kind of connection. Stability does not determine to whom justification is owed, but it might contribute to determining what is justifiable to citizens. (shrink)

This paper addresses the robust stabilization problem for a class of stochastic Markovian jump systems with distributed delays. The systems under consideration involve Brownian motion, Markov chains, distributed delays, and parameter uncertainties. By an appropriate Lyapunov–Krasovskii functional, the novel delay-dependent stabilization criterion for the stochastic Markovian jump systems is derived in terms of linear matrix inequalities. When given linear matrix inequalities are feasible, an explicit expression of the desired state feedback controller is given. The designed controller, based on the (...) obtained criterion, ensures asymptotically stable in the mean square sense of the resulting closed-loop system. The convenience of the design is greatly enhanced due to the existence of an adjustable parameter in the controller. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed theory. (shrink)

Several authors have investigated the question of whether canonical logic-based accounts of belief revision, and especially the theory of AGM revision operators, are compatible with the dynamics of Bayesian conditioning. Here we show that Leitgeb's stability rule for acceptance, which has been offered as a possible solution to the Lottery paradox, allows to bridge AGM revision and Bayesian update: using the stability rule, we prove that AGM revision operators emerge from Bayesian conditioning by an application of the principle (...) of maximum entropy. In situations of information loss, or whenever the agent relies on a qualitative description of her information state - such as a plausibility ranking over hypotheses, or a belief set - the dynamics of AGM belief revision are compatible with Bayesian conditioning; indeed, through the maximum entropy principle, conditioning naturally generated AGM revision operators. This mitigates an impossibility theorem of Lin and Kelly for tracking Bayesian conditioning with AGM revision, and suggests an approach to the compatibility problem that highlights the information loss incurred by acceptance rules in passing from probabilistic to qualitative representations of beliefs. (shrink)

This paper deals with the exponential stabilization problem for a class of nonlinear switched systems with mixed delays under asynchronous switching. The switching signal of the switched controller involves delay, which results in the asynchronous switching between the candidate controllers and subsystems. By constructing the parameter-dependent Lyapunov-Krasovskii functional and the average dwell time approach, some sufficient conditions in forms of linear matrix inequalities are presented to ensure the exponential stability of the switched nonlinear system under arbitrary switching signals. (...) In addition, through the special deformation of the matrix and Schur complement, the controllers with asynchronous switching are designed. Finally, a numerical example and a practical example of river pollution control are provided to show the validity and potential of the developed results. (shrink)

The topic of moral diversity is not only prevalent in contemporary moral and political philosophy, it is also practically relevant. Moral diversity, however, poses a significant challenge for moral theory building. John Thrasher, in his discussion of public reason theory, which includes social contract theory, argues that if one seriously considers the goal of moral constructivism and considerations of representation and stability, then moral diversity poses an insurmountable problem for most public reason theories. I agree with Thrasher that (...) moral diversity poses a significant challenge for orthodox multistage social contract theories. In fact, I even add a further problem for such theories under the assumption of deep moral diversity. Nevertheless, I argue that my recently developed multilevel social contract theory overcomes these problems. I focus on some of the underexplored features of this theory to show that multilevel social contract theory offers one conceptually coherent and plausible way to render social contract theory viable and relevant for modern diverse societies. (shrink)

The replicator dynamics and Moran process are the main deterministic and stochastic models of evolutionary game theory. The models are connected by a mean-field relationship—the former describes the expected behavior of the latter. However, there are conditions under which their predictions diverge. I demonstrate that the divergence between their predictions is a function of standard techniques used in their analysis and of differences in the idealizations involved in each. My analysis reveals problems for stochastic stability analysis in a broad (...) class of games, demonstrates a novel domain of agreement between the dynamics, and indicates a broader moral for evolutionary modeling. (shrink)

The problem of identity is central to epistemic transference. However, relative identity appears to be the only way to work out an epistemic useful notion of identity. Relative identity, on its part, is either parasitic on strict identity or not identity at all. If, on the contrary, we ought for a strict concept of identity capable of satisfying its requirements, we end up with a tautologic and epistemic worthless category. The paper provides an answer to this problem, which, (...) while working with a strict notion, shows how it might still serve epistemic purposes. In doing so, it shows how a formal reconstruction of our objectual world and the identities we refer to poses a workable model upon which our messy epistemic one acquires stability. The paper focuses primarily on the Geach-Quine discussion on identity. (shrink)

A perennial question of political thought is how to stabilize a just regime in the face of disagreement. The importance of this question has been heightened with the Weberian state that monopolizes the power of coercion and anchors society under a single governance structure. This political form has given us both liberal democracy and totalitarianism. The stakes could not be higher in ensuring stability without dismantling pluralism. This paper provides a novel solution to the stability problem by (...) focusing on dynamic stability reached through polycentric democracy. Plural and overlapping centers of governance characterize such democracy. This renders a polycentric system more resilient to changing views than a monocentric one and superior on political risk-management grounds by diffusing decision-making risks. A polycentric system also fosters antifragility in society by avoiding seeking a single and fixed point equilibrium, thereby eluding the pitfalls currently afflicting liberal democracy. (shrink)

The preferred basis problem has resisted resolution because it is doubly ill-posed. First, it seeks an ontological solution to a structural problem: every proposed solution encounters the same difficulty, indicating that its source is architectural rather than interpretive. Second, it demands an answer in the language of orthonormal bases, presupposing that classical alternatives must correspond to orthogonal decompositions of a state space. They need not. Classical worlds require only logical incompatibility of stabilized distinctions, not linear-algebraic orthogonality. This paper (...) develops refinement geometry, a theory-neutral structural framework that reframes rather than solves the preferred basis problem by identifying its root cause. Physical histories are partially ordered by prefix extension. Stability predicates are existential claims over history prefixes, necessarily monotone since what has occurred cannot be uncertified by later extension, and admissible only if their truth sets are open under finite variation. Monotonicity and admissibility together induce a directed refinement structure admitting a canonical maximal partition. The root cause is then identifiable: purely synchronic refinement cannot reproduce maximal refinement structure because admissible stability predicates are defined over history prefixes and carry monotone certification semantics that no instantaneous state description can fully encode. A synchronic procedure powerful enough to recover the canonical maximal partition must implicitly reconstruct and traverse the prefix order, collapsing into diachronic refinement in disguise rather than achieving a genuinely synchronic result. In contrast, diachronic refinement, accumulating certified distinctions monotonically along histories, converges to the canonical maximal partition without basis selection or orthogonality. Significantly, quantum interference requires no special treatment: non-singleton partition blocks represent histories not yet separated by any certified distinction. Decoherence generates the stability predicates that resolve such blocks; classical worlds are the limit of that resolution. Persistence of distinctions, irreversibility, and absence of merging follow from predicate semantics alone, independent of dynamical law and without presupposing Hilbert-space structure or ontological commitments. (shrink)

Let p be an odd prime. A method is described which given a structure M of finite similarity type produces a nilpotent group of class 2 and exponent p which is in the same stability class as M. Theorem. There are nilpotent groups of class 2 and exponent p in all stability classes. Theorem. The problem of characterizing a stability class is equivalent to characterizing the (nilpotent, class 2, exponent p) groups in that class.

In the work of both Ludwik Fleck and Thomas Kuhn the scientific literature plays important roles for stability and change of scientific phenomenal worlds. In this article we shall introduce the analyses of scientific literature provided by Fleck and Kuhn, respectively. From this background we shall discuss the problem of how divergent thinking can emerge in a dogmatic atmosphere. We shall argue that in their accounts of the factors inducing changes of scientific phenomenal worlds Fleck and Kuhn offer (...) substantially different approaches, and we shall discuss in which respects their approaches may be compatible. (shrink)

The problem of identity is central to epistemic transference. However, relative identity appears to be the only way to work out an epistemic useful notion of identity. Relative identity, on its part, is either parasitic on strict identity or not identity at all. If, on the contrary, we ought for a strict concept of identity capable of satisfying its requirements, we end up with a tautologic and epistemic worthless category. The paper provides an answer to this problem, which, (...) while working with a strict notion, shows how it might still serve epistemic purposes. In doing so, it shows how a formal reconstruction of our objectual world and the identities we refer to poses a workable model upon which our messy epistemic one acquires stability. The paper focuses primarily on the Geach-Quine discussion on identity. (shrink)

One important thesis Ásta defends in Categories We Live By is that social properties and categories are somehow dependent on our thoughts, attitudes, or practices—that they are inventions of the mind, projected onto the world. Another important aspect of her view is that the social properties are related to certain base properties; an individual is placed in a category when the relevant base properties are thought to hold of them. I see the relationship between the social and the base as (...) connected to the problem of explaining how the social properties are sufficiently stable so as to be taken seriously, both in theoretical endeavors as well as in practical matters of how we relate to each other. In this light, I identify stability constraints for an adequate account of social categories. I argue that certain distinctive aspects of Ásta's conferralist view of social categories, such as the radical contextualism in her account of gender, undermine the stability of categories and are at odds with taking social categories seriously. I end with the suggestion that a distinctive “sheltered” form of normativity might help us do justice to Ásta's insights while avoiding some of the destabilizing elements of conferralism. (shrink)

Public reason theories are characterized by three conditions: constructivism, representation, and stability. Constructivism holds that justification does not rely on any antecedent moral or political values outside of the procedure of agreement. Representation holds that the reasons for the choice in the model must be rationally explicable to real agents outside the model. Stability holds that the principles chosen in the procedure should be stable upon reflection, especially in the face of diversity in a pluralistic society. Choice procedures (...) that involve at least two-stages with different information, as Rawls’s theory does, will be path-dependent and not meet the condition of representation since it will not be globally coherent. Attempts to solve this problem without eliminating the segmentation of choice in the procedure will run afoul of constructivism or stability. This problem is instructive because it highlights how public reason theories must evolve in the face of increased concerns about diversity. (shrink)

Recent scholarship has drawn attention to John Rawls’s concern with stability—a concern that, as Rawls himself notes, motivated Part III of A Theory of Justice and some of the more important changes of his political turn. For Rawls, the possibility of achieving ‘stability for the right reasons’ depends on citizens possessing sufficient moral motivation. I argue, however, that the moral psychology Rawls develops to show how such motivation would be cultivated and sustained does not cohere with his specific (...) descriptions of ‘pluralist ’ doctrines. Considering Rawls’s claims that ‘most’ citizens—both in contemporary liberal democracies and in the well-ordered society—possess such doctrines, this incompatibility threatens to undermine his stability arguments. Despite the enormous importance of pluralist doctrines and the potential difficulties they pose for Rawls’s project, remarkably little attention has been paid to them. By critically examining these difficulties, the article begins to address this oversight. (shrink)

Since the appearance of Prior’s tonk, inferentialists tried to formulate conditions that a collection of inference rules for a logical constant has to satisfy in order to succeed in conferring an acceptable meaning to it. Dummett proposed a pair of conditions, dubbed ‘harmony’ and ‘stability’ that have been cashed out in terms of the existence of certain transformations on natural deduction derivations called reductions and expansions. A long standing open problem for this proposal is posed by quantum disjunction: (...) although its rules are intuitively unstable, they pass the test of existence of expansions. Although most authors view instabilities of this kind as too subtle to be detected by the requirement of existence of expansions, we first discuss a case showing that this requirement can indeed detect instabilities of this kind, and then show how the expansions for disjunction-like connectives have to be reformulated to rule out quantum disjunction. We show how the alternative pattern for expansions can be formulated for connectives and quantifiers whose rules satisfy a scheme originally developed by Prawitz and Schroeder-Heister. Finally we compare our proposal with a recent one due to Jacinto and Read. (shrink)

This essay examines the problems associated with the installation of a precision instrument at the National Astronomical Observatory of Chile, starting before its construction and following the process through its installation to its later useful life. Between 1908 and 1913, the director of the observatory, Friedrich W. Ristenpart, corresponded with the German manufacturer, A. Repsold & Söhne in Hamburg, trying to identify the critical points pertinent to the installation of the instrument in Chile. These communications reveal how the installation of (...) the instrument required the stabilization of local knowledge (location, adjustment, calibration, and staging) that would allow the data it obtained to be universally validated. This correspondence between user and manufacturer also reveals that the phenomenon of the mobility of instruments implies much more than simply transporting something from one place to another: there is no movement without some type of coordination between the extraction of an object from a certain place and context and its insertion into a new place and set of relationships. (shrink)

Companies in the stability operations industry have been subjected to painstaking scrutiny while critics have ignored the value they bring to contingency operations and government clients. Moreover, the scope of the industry is often overlooked by critics who paint a picture of uncontrollable companies making ridiculous profits. In response, this article offers some insight on stability operations, contracting processes, pitfalls, and opportunities. The article then discusses some of the criticisms that surround the industry. These criticisms are often due (...) to sensationalized reporting, and a significant problem is that reports on criminal activity such as fraud and abuse are exaggerated. In contrast, the far larger problem of waste due to poor client planning and oversight is glossed over. Finally, the article discusses industry self-policing efforts that have emerged to support the use of professional and compliant businesses in stability operations. Ultimately it is governmental regulatory enforcement and quality contracting practices that will do the most to marginalize unethical companies, reward better firms, and improve partnerships and success rates in stability operations globally. (shrink)

In this paper, dynamic behavior analysis has been discussed for a class of switched complex-valued neural networks with interval parameter uncertainties and impulse disturbance. Sufficient conditions for guaranteeing the existence, uniqueness, and global robust exponential stability of the equilibrium point have been obtained by using the homomorphism mapping theorem, the scalar Lyapunov function method, the average dwell time method, and M-matrix theory. Since there is no result concerning the stability problem of switched neural networks defined in complex (...) number domain, the stability results we describe in this paper generalize the existing ones. The effectiveness of the proposed results is illustrated by a numerical example. (shrink)

The article examines the principles of stability and civil disobedience in unity to contrast them with a current idea that the principle of peace is a formal ideal of law, while justice is its substantive but relative ideal. The proposed alternative, emphasizing the problems of stability, highlights its conceptual uniqueness and its political significance, which theories of justice and theories of peace, but also theories of law, do not pay attention to.

The article investigates the different conceptions of stability found in qualitative studies on the solutions of differential equations. We start from the definitions proposed by Poincaré and criticized by Birkhoff for not being fully qualitative, and show that the clarification of the criterion for stating that a property is qualitative comes precisely with Birkhoff. In addition, we note that the stability conceptions of Lyapunov and Levi-Civita are also important in this transition from the appearance of the first qualitative (...) tools in the study of differential equations to the definition of stability in use in dynamical systems theory. The history of stability can help to explain the meaning of the word “qualitative” in this context. (shrink)

Examines the relation between two of the most influential Kantian works in political philosophy in this century, John Rawls's _A Theory of Justice_ and his _Political Liberalism_. The rationale for Rawls's shift in position from the earlier book to the later, it is argued, is a recognized need to satisfy a deeply Kantian requirement on the legitimate exercise of state coercive power. In a pluralistic world where reasonable people differ about the truth of religion and morality, the requirement can be (...) met only by showing the possibility of an overlapping consensus on shared political principles. Contrary to what Rawls at times suggests, the reason for his move from a ‘comprehensive moral theory’ to a ‘political conception’ of justice was not an (perhaps doubtful) expectation that consensus on his principles would be a stabilizing force, but instead a recognition of the need to provide a justification of these principles that is respectful of the diversity of moral and religious opinions among reasonable people. (shrink)

This chapter explores an apparent paradox of stability and change in patient safety thinking and practice. While dominant approaches to patient safety portray healthcare systems as relatively stable, medical errors as preventable and standardization as the pre-eminent solution to safety problems, a new resilience engineering approach—Safety II—presents safety as the ability to adapt to ever-changing and complex surroundings. By analysing a factor-ten drug prescription error and the subsequent root cause analysis, Pedersen examines how available approaches to patient safety management (...) reproduce an illusion of certainty by maintaining a separation of stabile and changing healthcare settings. In response, John Dewey (Experience and Nature. New York: Dover Publications, 1925) and Charles Perrow (Complex Organizations: A Critical Essay. USA: McGraw-Hill Publishers, 1972; Normal Accidents: Living with High-Risk Technologies. Princeton, NJ: Princeton University Press, 1984) are cited for suggesting a more subtle and mutually constituent relationship between rules and discretion, standards and flexibility. (shrink)

In this commentary on Rotts paper Stability, Strength and Sensitivity: Converting Belief into Knowledge, I discuss two problems of the stability theory of knowledge which are pointed out by Rott. I conclude that these problems offer no reason for rejecting the stability theory, but might be grounds for deviating from the standard AGM account of belief revision which Rott presupposes.

Standard adaptive control is the preferred approach for stabilization and synchronization of chaotic systems when the structure of such systems is a priori known but the parameters are unknown. However, in the presence of unmodeled dynamics and/or disturbance, this approach is not effective anymore due to the drift of the parameter estimations, which eventually causes the instability of the closed-loop system. In this paper, a robustifying term, which consists of a saturation function, is used to avoid this problem. The (...) robustifying term is added to the adaptive control law. Consequently, the learning law is also modified. The boundedness of the states and the parameter estimations is rigorously and thoroughly proven by means of Lyapunov like analysis based on Barbalat’s lemma. On these new conditions, the convergence to zero cannot be achieved due to the presence of unmodeled dynamics and/or disturbance. However, it is still possible to guarantee the asymptotic convergence to a bounded zone around zero. The width of this zone can be adjusted by the designer. The performance of this robust approach is verified by numerical simulations. Although, for simplicity, this strategy is only applied to the stabilization and synchronization of Zhang system, the procedure can easily be generalized to a broad class of chaotic systems. (shrink)

ArgumentFor more than thirty years after World War II, the unconventional economist Kenneth E. Boulding was a fervent advocate of the integration of the social sciences. Building on common general principles from various fields, notably economics, political science, and sociology, Boulding claimed that an integrated social science in which mental images were recognized as the main determinant of human behavior would allow for a better understanding of society. Boulding's approach culminated in the social triangle, a view of society as comprised (...) of three main social organizers – exchange, threat, and love – combined in varying proportions. According to this view, the problems of American society were caused by an unbalanced combination of these three organizers. The goal of integrated social scientific knowledge was therefore to help policy makers achieve the “right” proportions of exchange, threat, and love that would lead to social stabilization. Though he was hopeful that cross-disciplinary exchanges would overcome the shortcomings of too narrow specialization, Boulding found that rather than being the locus of a peaceful and mutually beneficial exchange, disciplinary boundaries were often the occasion of conflict and miscommunication. (shrink)