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A crude look at the whole : the science of complex systems in business, life, and society
\"Imagine trying to understand a stained glass window by breaking it into pieces and examining it one shard at a time. While you could probably learn a lot about each piece, you would have no idea about what the entire picture looks like. This is reductionism--the idea that to understand the world we only need to study its pieces--and it is how most social scientists approach their work. In [this book], social scientist and economist John H. Miller shows why we need to start looking at whole pictures. For one thing, whether we are talking about stock markets, computer networks, or biological organisms, individual parts only make sense when we remember that they are part of larger wholes. And perhaps more importantly, those wholes can take on behaviors that are strikingly different from that of their pieces\"--Amazon.com.
Book
Laminational Models for Some Spaces of Polynomials of Any Degree
The so-called “pinched disk” model of the Mandelbrot set is due to A. Douady, J. H. Hubbard and W. P. Thurston. It can be described
in the language of geodesic laminations. The combinatorial model is the quotient space of the unit disk under an equivalence relation
that, loosely speaking, “pinches” the disk in the plane (whence the name of the model). The significance of the model lies in particular
in the fact that this quotient is planar and therefore can be easily visualized. The conjecture that the Mandelbrot set is actually
homeomorphic to this model is equivalent to the celebrated MLC conjecture stating that the Mandelbrot set is locally connected.
For parameter spaces of higher degree polynomials no combinatorial model is known. One possible reason may be that the higher degree
analog of the MLC conjecture is known to be false. We investigate to which extent a geodesic lamination is determined by the location of
its critical sets and when different choices of critical sets lead to essentially the same lamination. This yields models of various
parameter spaces of laminations similar to the “pinched disk” model of the Mandelbrot set.
eBook
Optimization of identifiability for efficient community detection
Many physical and social systems are best described by networks. And the structural properties of these networks often critically determine the properties and function of the resulting mathematical models. An important method to infer the correlations between topology and function is the detection of community structure, which plays a key role in the analysis, design, and optimization of many complex systems. The nonnegative matrix factorization has been used prolifically to that effect in recent years, although it cannot guarantee balanced partitions, and it also does not allow a proactive computation of the number of communities in a network. This indicates that the nonnegative matrix factorization does not satisfy all the nonnegative low-rank approximation conditions. Here we show how to resolve this important open problem by optimizing the identifiability of community structure. We propose a new form of nonnegative matrix decomposition and a probabilistic surrogate learning function that can be solved according to the majorization-minimization principle. Extensive in silico tests on artificial and real-world data demonstrate the efficient performance in community detection, regardless of the size and complexity of the network.
Journal Article
A complex systems approach to the study of change in psychotherapy
Background
A growing body of research highlights the limitations of traditional methods for studying the process of change in psychotherapy. The science of complex systems offers a useful paradigm for studying patterns of psychopathology and the development of more functional patterns in psychotherapy. Some basic principles of change are presented from subdisciplines of complexity science that are particularly relevant to psychotherapy: dynamical systems theory, synergetics, and network theory. Two early warning signs of system transition that have been identified across sciences (critical fluctuations and critical slowing) are also described. The network destabilization and transition (NDT) model of therapeutic change is presented as a conceptual framework to import these principles to psychotherapy research and to suggest future research directions.
Discussion
A complex systems approach has a number of implications for psychotherapy research. We describe important design considerations, targets for research, and analytic tools that can be used to conduct this type of research.
Conclusions
A complex systems approach to psychotherapy research is both viable and necessary to more fully capture the dynamics of human change processes. Research to date suggests that the process of change in psychotherapy can be nonlinear and that periods of increased variability and critical slowing might be early warning signals of transition in psychotherapy, as they are in other systems in nature. Psychotherapy research has been limited by small samples and infrequent assessment, but ambulatory and electronic methods now allow researchers to more fully realize the potential of concepts and methods from complexity science.
Journal Article
Extracting the Multiscale Backbone of Complex Weighted Networks
A large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength. In recent years, the study of an increasing number of large-scale networks has highlighted the statistical heterogeneity of their interaction pattern, with degree and weight distributions that vary over many orders of magnitude. These features, along with the large number of elements and links, make the extraction of the truly relevant connections forming the network's backbone a very challenging problem. More specifically, coarse-graining approaches and filtering techniques come into conflict with the multiscale nature of large-scale systems. Here, we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks, preserving the edges that represent statistically significant deviations with respect to a null model for the local assignment of weights to edges. An important aspect of the method is that it does not belittle small-scale interactions and operates at all scales defined by the weight distribution. We apply our method to realworld network instances and compare the obtained results with alternative backbone extraction techniques.
Journal Article
Emergence in marketing: an institutional and ecosystem framework
Many core marketing concepts (e.g., markets, relationships, customer experience, brand meaning, value) concern phenomena that are difficult to understand using linear and dyadic approaches, because they are emergent. That is, they arise, often unpredictably, from interactions within complex and dynamic contexts. This paper contributes to the marketing discipline through an explication of the concept of emergence as it applies to marketing theory. We accomplish this by first drawing on the existing literature on emergence in philosophy, sociology, and the theory of complex adaptive systems, and then link and extend this understanding to marketing using the theoretical framework of service-dominant (S-D) logic, particularly as enhanced by its service-ecosystems and institutionalization perspectives. Our work recognizes both emergence and institutionalization as integral or interrelated processes in the creation, maintenance, and disruption of markets and marketing phenomena. We conclude by discussing implications for marketing research and practice.
Journal Article
Why the Mittag-Leffler Function Can Be Considered the Queen Function of the Fractional Calculus?
In this survey we stress the importance of the higher transcendental Mittag-Leffler function in the framework of the Fractional Calculus. We first start with the analytical properties of the classical Mittag-Leffler function as derived from being the solution of the simplest fractional differential equation governing relaxation processes. Through the sections of the text we plan to address the reader in this pathway towards the main applications of the Mittag-Leffler function that has induced us in the past to define it as the Queen Function of the Fractional Calculus. These applications concern some noteworthy stochastic processes and the time fractional diffusion-wave equation We expect that in the future this function will gain more credit in the science of complex systems. Finally, in an appendix we sketch some historical aspects related to the author’s acquaintance with this function.
Journal Article
Common neighbours and the local-community-paradigm for topological link prediction in bipartite networks
Bipartite networks are powerful descriptions of complex systems characterized by two different classes of nodes and connections allowed only across but not within the two classes. Unveiling physical principles, building theories and suggesting physical models to predict bipartite links such as product-consumer connections in recommendation systems or drug-target interactions in molecular networks can provide priceless information to improve e-commerce or to accelerate pharmaceutical research. The prediction of nonobserved connections starting from those already present in the topology of a network is known as the link-prediction problem. It represents an important subject both in many-body interaction theory in physics and in new algorithms for applied tools in computer science. The rationale is that the existing connectivity structure of a network can suggest where new connections can appear with higher likelihood in an evolving network, or where nonobserved connections are missing in a partially known network. Surprisingly, current complex network theory presents a theoretical bottle-neck: a general framework for local-based link prediction directly in the bipartite domain is missing. Here, we overcome this theoretical obstacle and present a formal definition of common neighbour index and local-community-paradigm (LCP) for bipartite networks. As a consequence, we are able to introduce the first node-neighbourhood-based and LCP-based models for topological link prediction that utilize the bipartite domain. We performed link prediction evaluations in several networks of different size and of disparate origin, including technological, social and biological systems. Our models significantly improve topological prediction in many bipartite networks because they exploit local physical driving-forces that participate in the formation and organization of many real-world bipartite networks. Furthermore, we present a local-based formalism that allows to intuitively implement neighbourhood-based link prediction entirely in the bipartite domain.
Journal Article