This research is motivated by the program of Reverse Mathematics. We investigate basic part of complex analysis within some weak subsystems of second order arithmetic, in order to determine what kind of set existence axioms are needed to prove theorems of basic analysis. We are especially concerned with Cauchy’s integral theorem. We show that a weak version of Cauchy’s integral theorem is proved in RCAo. Using this, we can prove that holomorphic functions are analytic in RCAo. On (...) the other hand, we show that a full version of Cauchy’s integral theorem cannot be proved in RCAo but is equivalent to weak König’s lemma over RCAo. (shrink)

Leech et al. present a connectionist algorithm as a model of (the development) of analogizing, but they do not specify the algorithm's associated computational-level theory, nor its computational complexity. We argue that doing so may be essential for connectionist cognitive models to have full explanatory power and transparency, as well as for assessing their scalability to real-world input domains.

This study is based on the situation of Taiwan listed companies as derivative financial products from 2015 to 2017, analyzing the relationship between the hedging of derivative financial products and characteristics of enterprises and the factors that affect the hedging decision-making of companies. It is found that even after the announcement of Taiwan’s No. 34 and No. 36 bulletins, there are still some problems that are needed to improve in the disclosure of derivative financial product investment information by Taiwan’s listed (...) companies, at least in the disclosure of the reasons for this conduct which is still insufficient. In this study, two-stage regression analysis method is applied to empirical analysis, and it is found that hedging activities are related to corporate characteristics, such as expected financial crisis costs, corporate size, equity issues, growth investment opportunities, and information asymmetry. In the investment of derivative financial products, enterprises should evaluate their own financial characteristics as a reference for the risk avoidance decision. At the same time, it is necessary to investigate different natures of hedging tools used in appropriate risk categories, so as to fully achieve the hedging effect and maximize the hedging benefits. This study also found that companies with higher growth investment opportunities, larger size, and higher financial crisis costs will tend to use derivative financial products for hedging. As for the impact of other industries, it is found that the electronic and electrical machinery industries are more active than other industries in hedging behaviors of undertaking derivative financial products’ transaction. (shrink)

Tanabe Hajime (1885-1962) in his later years explored the so-called "dialectical" interpretation of complex analysis, an important part of his philosophy of mathematics that has previously been criticized as lacking mathematical accuracy and philosophical importance. I interpret his elaboration on complex analysis as an attempt to develop Leibniz's theory of individual notion and to supplement Hegel's view of higher analysis with the development in mathematics such as the theory of analytic continuation and Riemann surface. This (...) interpretation shows the previously underrated philosophico-mathematical significance of Tanabe's argument. (shrink)

This work introduces a three-dimensional, highly nonlinear quadratic oscillator with no linear terms in its equations. Most of the quadratic ordinary differential equations such as Chen, Rossler, and Lorenz have at least one linear term in their equations. Very few quadratic systems have been introduced and all of their terms are nonlinear. Considering this point, a new quadratic system with no linear term is introduced. This oscillator is analyzed by mathematical tools such as bifurcation and Lyapunov exponent diagrams. It is (...) revealed that this system can generate different behaviors such as limit cycle, torus, and chaos for its different parameters’ sets. Besides, the basins of attractions for this system are investigated. As a result, it is revealed that this system’s attractor is self-excited. In addition, the analog circuit of this oscillator is designed and analyzed to assess the feasibility of the system’s chaotic solution. The PSpice simulations confirm the theoretical analysis. The oscillator’s time series complexity is also investigated using sample entropy. It is revealed that this system can generate dynamics with different sample entropies by changing parameters. Finally, impulsive control is applied to the system to represent a possible solution for stabilizing the system. (shrink)

Intractability is a growing concern across the cognitive sciences: while many models of cognition can describe and predict human behavior in the lab, it remains unclear how these models can scale to situations of real-world complexity. Cognition and Intractability is the first book to provide an accessible introduction to computational complexity analysis and its application to questions of intractability in cognitive science. Covering both classical and parameterized complexity analysis, it introduces the mathematical concepts and proof techniques that can (...) be used to test one's intuition of tractability. It also describes how these tools can be applied to cognitive modeling to deal with intractability, and its ramifications, in a systematic way. Aimed at students and researchers in philosophy, cognitive neuroscience, psychology, artificial intelligence, and linguistics who want to build a firm understanding of intractability and its implications in their modeling work, it is an ideal resource for teaching or self-study. (shrink)

In this paper, a discrete-time dynamic duopoly model, with nonlinear demand and cost functions, is established. The properties of existence and local stability of equilibrium points have been verified and analyzed. The stability conditions are also given with the help of the Jury criterion. With changing of the values of parameters, the system shows some new and interesting phenomena in terms to stability and multistability, such as V-shaped stable structures and different shape basins of attraction of coexisting attractors. The eye-shaped (...) structures appear where the period-doubling and period-halving bifurcations occur. Finally, by utilizing critical curves, the changes in the topological structure of basin of attraction and the reason of “holes” formation are analyzed. As a result, the generation of global bifurcation, such as contact bifurcation or final bifurcation, is usually accompanied by the contact of critical curves and boundary. (shrink)

All projects take place within a context of uncertainty. That is especially noticeable in complex hydroelectric power generation projects, which are affected by factors such as the large number of multidisciplinary tasks to be performed in parallel, long execution times, or the risks inherent in various fields like geology, hydrology, and structural, electrical, and mechanical engineering, among others. Such factors often lead to cost overruns and delays in projects of this type. This paper analyzes the efficiency of the Earned (...) Value Management technique and its Earned Schedule extension, as means of forecasting costs and deadlines when applied to complex hydroelectric power production projects. It is worth noting that this analysis was based on simulation models applied to real-life projects. The results showed that cost forecasting becomes very accurate over time, whereas duration forecasting is not reliably accurate. (shrink)

Sufficient conditions for first-order-based sequent calculi to admit cut elimination by a Schütte–Tait style cut elimination proof are established. The worst case complexity of the cut elimination is analysed. The obtained upper bound is parameterized by a quantity related to the calculus. The conditions are general enough to be satisfied by a wide class of sequent calculi encompassing, among others, some sequent calculi presentations for the first order and the propositional versions of classical and intuitionistic logic, classical and intuitionistic modal (...) logic S4, and classical and intuitionistic linear logic and some of its fragments. Moreover the conditions are such that there is an algorithm for checking if they are satisfied by a sequent calculus. (shrink)

The processes in construction are more likely than others to breed unsafe behaviors, and the consequences of these actions can be serious. This paper first reviews the research status on unsafe behavior in construction teams. It then analyzes the complex mechanisms that lead to unsafe behavior and constructs a three-layer structural model based on agent-based modeling technology. This modeling deals with complexity and elaborates on key points and potential research ideas in the study of unsafe behavior in construction teams. (...) Using the ABM method, the effects of different incentive strategies on the safe behavior of construction teams under different management scenarios were studied. The results showed that when members have a fair perception of the situation, the effect of the excess performance reward distribution, according to the member’s safety awareness level, is better than the average distribution effect. This is the case whether the member’s safety behavior level is positively or negatively related to the member’s safety awareness level. This study proves the feasibility, validity, and universality of the three-layer structural model. It also reaches certain management conclusions and ideas for further development. The purpose of this paper is to provide a reference for research on the containment and prevention of unsafe behavior in construction teams. (shrink)

This study examined the influence of the executive board of directors’ gender diversity on the financial performance of listed companies on the Bucharest Stock Exchange, for the period 2011 to 2019. The analysis of the composition and different characteristics of the board and the executive directors proved to be effective tools for corporate governance in countries with an emerging capital market. Therefore, a disclosure index on directors’ characteristics was used to moderate the interaction between gender diversity and financial performance, (...) based on the theoretical framework provided by upper echelon theory. The study contributes to the enrichment of the literature both by using the composite indicator built by applying the multiway PCA method on panel data to express financial performance and by designing the ten EGLS panel models involving five financial indicators and two proxies for gender diversity. The results showed that there is a positive impact of the proportion of women on the executive board of directors on financial performance, measured through the composite index, ROA, ROE, and SOL. A statistically significant impact of gender diversity on financial performance was found only for SOL, in the case of the Blau index. Also, using the random-effects model to perform the panel data analysis, the results showed that a higher executive board size can be associated with better financial performance measured through the composite index, ROA, ROE, and EPS. Practical implications are significant for the board of executives’ composition, the complexity of the relationship with the board, and reshaping governance practices. (shrink)

According to Leibniz’s infinite-analysis account of contingency, any derivative truth is contingent if and only if it does not admit of a finite proof. Following a tradition that goes back at least as far as Bertrand Russell, several interpreters have been tempted to explain this biconditional in terms of two other principles: first, that a derivative truth is contingent if and only if it contains infinitely complex concepts and, second, that a derivative truth contains infinitely complex concepts (...) if and only if it does not admit of a finite proof. A consequence of this interpretation is that Leibniz’s infinite-analysis account of contingency falls prey to Robert Adams’s Problem of Lucky Proof. I will argue that this interpretation is mistaken and that, once it is properly understood how the idea of an infinite proof fits into Leibniz’s circle of modal notions, the problem of lucky proof simply disappears. (shrink)

Globalization is a ubiquitousyet highly elusive term. The debate on the cont and meaning of globalization is still waged largely in binary terms; for example, globalization is understood either as increasing standardization or as increasing difference. This article argues that the effects of globalization are best understood in terms of the following three sets of simultaneous contradictions: convergence and divergence, inclusion and exclusion, and centralization and decentralization. These contradictions can be fruitfully “unpacked” and examined through critical stakeholder analysis (CSA). (...) This technique focuses on broader structural commonalties and differences among key stakeholder groups, factors that are not incorporated in mainstream stakeholder theory. The associated normative agenda of CSA promotes a common understanding of key issues within a focal organizational field, the negotiated settlement of zero-sum situations that optimize collective stakeholder interests within that field, and the containment and minimization of negative externalities within as well as between fields. (shrink)

Network analysis views complex systems as networks with well-defined structural properties that account for their complexity. These characteristics, which include scale-free behavior, small worlds and communities, are not to be found in networks such as random graphs and lattices that do not correspond to complex systems. They provide therefore a robust ground for claiming the existence of “complex networks” as a non-trivial subset of networks. The theory of complex networks has thus been successful in making (...) systematically explicit relevant marks of complexity in the form of structural properties, and this success is at the root of its current popularity. Much less systematic has been, on the other hand, the definition of the properties of the building components of complex networks. The obvious assumption is that these components must be nodes and links. Generally, however, the internal structure of nodes is not taken into account, and links are serendipitously identified by the perspective with which one looks at the network to be analyzed. For instance, if the nodes are Web pages that contain information about scientific papers, one point of view will match the relevant links with hyperlinks to similar Web pages, and another with citations of other articles. We intend to contribute here a systematic approach to the identification of the components of a complex network that is based on information theory. The approach hinges on some recent results arising from the convergence between the theory of complex networks and probabilistic techniques for content mining. At its core there is the idea that nodes in a complex network correspond to basic information units from which links are extracted via methods of machine learning. Hence the links themselves are viewed as emergent properties, similarly to the broader structural properties mentioned above. Indeed, beside rounding up the theory, this approach based on learning has clear practical benefits, in that it makes networks emerge from arbitrary information domains. We provide examples and applications in a variety of contexts, starting from an information-theoretic reconstruction of the well-known distinction between “strong links” and “weak links” and then delving into specific applications such as business process management and analysis of policy making. (shrink)

Entropy-based algorithms have been suggested as robust estimators of electroencephalography (EEG) predictability or regularity. This study aimed to examine possible disturbances in EEG complexity as a means to elucidate the pathophysiological mechanisms in chronic stroke, before and after a brain computer interface (BCI)-motor observation intervention. Eleven chronic stroke subjects and nine unimpaired subjects were recruited to examine the differences in their EEG complexity. The BCI-motor observation intervention was designed to promote functional recovery of the hand in stroke subjects. Fuzzy approximate (...) entropy (fApEn), a novel entropy-based algorithm designed to evaluate complexity in physiological systems, was applied to assess the EEG signals acquired from unimpaired subjects and stroke subjects, both before and after training. The results showed that stroke subjects had significantly lower EEG fApEn than unimpaired subjects (p < 0.05) in the motor cortex area of the brain (C3, C4, FC3, FC4, CP3, CP4) in both hemispheres before training. After training, motor function of the paretic upper limb, assessed by the Fugl-Meyer Assessment-Upper Limb (FMA-UL), Action Research Arm Test (ARAT), and Wolf Motor Function Test (WMFT) improved significantly (p < 0.05). Furthermore, the EEG fApEn in stroke subjects increased considerably in the central area of the contralesional hemisphere after training (p < 0.05). A significant correlation was noted between clinical scales (FMA-UL, ARAT, and WMFT) and EEG fApEn in C3/C4 in the contralesional hemisphere (p < 0.05). This finding suggests that the increase in EEG fApEn could be an estimator of the variance in upper limb motor function improvement. In summary, fApEn can be used to identify abnormal EEG complexity in chronic stroke, when used with BCI-motor observation training. Moreover, these findings based on the fApEn of EEG signals also expand the existing interpretation of training-induced functional improvement in stroke subjects. Entropy-based analysis might serve as a novel approach to understanding the abnormal cortical dynamics of stroke and the neurological changes induced by rehabilitation training. (shrink)

The emergence of conflicts between environmental safety incidents and protection rights generates sizeable political costs, which endangers the legitimacy of the government as well as political security and stability. This article further examines the role of political costs in environmental issues. First, political costs in relation to environmental issues are defined. An equilibrium strategic analysis is then presented using an evolutionary game model in which the strategic behavioral choices of government, enterprises, and citizens are investigated by embedding political costs (...) in the environmental governance system. Furthermore, the small-signal model was innovatively applied to simulate and analyze the stability of political costs under different equilibrium strategies in the system. The results show the following. Pubic behavior and government are the dominant factors that impact stability and instability, respectively. Public behavior is the core element that affects political cost consumption. When political costs are extremely depleted, the public will neglect economic interests, turn toward environmental interests, and choose the negative participation strategy, which destabilizes the system. The political cost signal at the optimal equilibrium point not only warns the government not to take the desperate action of concealing information asymmetry but also allows the government to let go of its hands to deal with the environmental issues. Corresponding policy recommendations are proposed. (shrink)

An analysis of two heuristic strategies for the development of mechanistic models, illustrated with historical examples from the life sciences. In Discovering Complexity, William Bechtel and Robert Richardson examine two heuristics that guided the development of mechanistic models in the life sciences: decomposition and localization. Drawing on historical cases from disciplines including cell biology, cognitive neuroscience, and genetics, they identify a number of "choice points" that life scientists confront in developing mechanistic explanations and show how different choices result in (...) divergent explanatory models. Describing decomposition as the attempt to differentiate functional and structural components of a system and localization as the assignment of responsibility for specific functions to specific structures, Bechtel and Richardson examine the usefulness of these heuristics as well as their fallibility—the sometimes false assumption underlying them that nature is significantly decomposable and hierarchically organized. When Discovering Complexity was originally published in 1993, few philosophers of science perceived the centrality of seeking mechanisms to explain phenomena in biology, relying instead on the model of nomological explanation advanced by the logical positivists (a model Bechtel and Richardson found to be utterly inapplicable to the examples from the life sciences in their study). Since then, mechanism and mechanistic explanation have become widely discussed. In a substantive new introduction to this MIT Press edition of their book, Bechtel and Richardson examine both philosophical and scientific developments in research on mechanistic models since 1993. (shrink)

Relational complexity provides a metric for measuring task demands, and in this respect has much in common with the cognitive complexity and control theory. However, relational complexity does not account for the relative difficulty of different relational types, and appears to underestimate the importance of changes in children's ability to act on the basis of their understanding.

Mental fatigue (MF) jeopardizes performance and safety through a variety of cognitive impairments and according to the complexity loss theory, should represent “complexity loss” in electroencephalogram (EEG). However, the studies are few and inconsistent concerning the relationship between MF and loss of complexity, probably because of the susceptibility of brain waves to noise. In this study, MF was induced in thirteen male college students by a simulated flight task. Before and at the end of the task, spontaneous EEG and auditory (...) steady-state response (ASSR) were recorded and instantaneous frequency variation (IFV) in alpha rhythm was extracted and analyzed by multiscale entropy (MSE) analysis. The results show that there were significant differences in IFV in alpha rhythm either from spontaneous EEG or from ASSR for all subjects. Therefore, the proposed method can be effective in revealing the complexity loss caused by MF in spontaneous EEG and ASSR, which may serve as a promising analyzing method to mark mild mental impairments. (shrink)

This article explores the affinities and parallels between Foucault's Nietzschean view of history and models of complexity developed in the physical sciences in the twentieth century. It claims that Foucault's rejection of structuralism and Marxism can be explained as a consequence of his own approach which posits a radical ontology whereby the conception of the totality or whole is reconfigured as an always open, relatively borderless system of infinite interconnections, possibilities and developments. His rejection of Hegelianism, as well as of (...) other enlightenment philosophies, can be understood at one level as a direct response to his rejection of the mechanical atomist, and organicist epistemological world views, based upon a Newtonian conception of a closed universe operating upon the basis of a small number of invariable and universal laws, by which all could be predicted and explained. The idea of a fully determined, closed universe is replaced; and in a way parallel to complexity theories, Foucault's own approach emphasises notions such as self‐organisation and dissipative structures; time as an irreversible, existential dimension; a world of finite resources but with infinite possibilities for articulation, or re‐investment; and characterised by the principles of openness, indeterminism, unpredictability, and uncertainty. The implications of Foucault's type of approach are then explored in relation to identity, creativity, and the uniqueness of the person. The article suggests that within a complexity theory approach many of the old conundrums concerning determinism and creativity, social constructionism and uniqueness, can be overcome. (shrink)

Wherever we look, we notice complexity. Philosophically, the concept constitutes a tangled web of problems, in theory as well as daily life. Complexity and Analysis is a meticulous rendering of these problems, tackling the seldom considered nature of complexity that confronts ontological analysts and holists alike. Stewart Umphrey expertly describes the limits of analysis as they have come to light within mathematics, the natural sciences, and analytic philosophy, explaining how Aristotle came upon, and sought to move beyond, the (...) limits of ontological analysis. In trying to understand any complex entity, Umphrey argues, one succeeds in meeting the criterion of metaphysical adequacy only if one fails to meet the crietrion of epistemological adequacy. Ranging across an array of subjects including Kantian and Hegelian idealism, this book provides a superb account of how our own complexity presents not only theoretical problems, but ethical and political dilemmas of great practical significance. (shrink)

Biological systems exhibit complexity at all levels of organization. It has recently been argued by Michael Behe that at the biochemical level a type of complexity exists--irreducible complexity--that cannot possibly have arisen as the result of natural, evolutionary processes and must instead be the product of (supernatural) intelligent design. Recent work on self-organizing chemical reactions calls into question Behe's analysis of the origins of biochemical complexity. His central interpretative metaphor for biochemical complexity, that of the well-designed mousetrap that ceases (...) to function if critical parts are absent, is undermined by the observation that typical biochemical systems exhibit considerable redundancy and overlap of function. Real biochemical systems, we argue, manifest redundant complexity--a characteristic result of evolutionary processes. (shrink)