Information and Self-Organization II: Steady State and Phase Transition

A Synergistic Approach towards Optimization of Coupled Cluster Amplitudes by Exploiting Dynamical Hierarchy

The coupled cluster iteration scheme for determining the cluster amplitudes involves a set of nonlinearly coupled difference equations. In the space spanned by the amplitudes, the set of equations are analyzed as a multivariate time-discrete map where the concept of time appears in an implicit manner. With the observation that the cluster amplitudes have difference in their relaxation timescales with respect to the distributions of their magnitudes, the coupled cluster iteration dynamics are considered as a synergistic motion of coexisting slow and fast relaxing modes, manifesting a dynamical hierarchical structure. With the identification of the highly damped auxiliary amplitudes, their time variation can be neglected compared to the principal amplitudes which take much longer time to reach the fixed points. We analytically establish the adiabatic approximation where each of these auxiliary amplitudes are expressed as unique parametric functions of the collective principal amplitudes, allowing us to study the optimization with the latter taken as the independent degrees of freedom. Such decoupling of the amplitudes significantly reduces the computational scaling without sacrificing the accuracy in the ground state energy as demonstrated by a number of challenging molecular applications. A road-map to treat higher order post-adiabatic effects is also discussed.

Towards a Link between Quantitative and Qualitative Sciences to Understand Social Systems Using the Example of Informal Settlements

Urbanization is one of the defining trends of our time and appropriate models are needed to anticipate the changes in cities, which are largely determined by human behavior. In the social sciences, where the task of describing human behavior falls, a distinction is made between quantitative and qualitative approaches, each of which has its own advantages and disadvantages. While the latter often provide descriptions of exemplary processes in order to describe phenomena as holistically as possible, the goal of mathematically motivated modeling is primarily to make a problem tangible. Both approaches are discussed in terms of the temporal evolution of one of the dominant settlement types in the world today: informal settlements. These areas have been modeled in conceptual works as self-organizing entities and in mathematical works as Turing systems. It is shown that the social issues surrounding these areas need to be understood both qualitatively and quantitatively. Inspired by the philosopher C. S. Peirce, a framework is proposed in which the various modeling approaches describing these settlements can be combined to arrive at a more holistic understanding of this phenomenon by using the language of mathematical modeling.

Interpersonal synchrony when singing in a choir

Singing in a choir has long been known to enhance well-being and protect mental health. Clearly, the experience of a uniquely harmonious social activity is very satisfying for the singers. How might this come about? One of the important factors positively associated with well-being is interpersonal action coordination allowing the choir to function as a whole. This review focuses on temporal coordination dynamics of physiological systems and/or subsystems forming part or the core of the functional substrate of choir singing. These coordination dynamics will be evaluated with respect to the concept of a superordinate system, or superorganism, based on the principles of self-organization and circular causality. We conclude that choral singing is a dynamic process requiring tight interpersonal action coordination that is characterized by coupled physiological systems and specific network topology dynamics, representing a potent biomarker for social interaction.

Catastrophe Theory Applied to Neuropsychological Data: Nonlinear Effects of Depression on Financial Capacity in Amnestic Mild Cognitive Impairment and Dementia

Financial incapacity is one of the cognitive deficits observed in amnestic mild cognitive impairment and dementia, while the combined interference of depression remains unexplored. The objective of this research is to investigate and propose a nonlinear model that explains empirical data better than ordinary linear ones and elucidates the role of depression. Four hundred eighteen (418) participants with a diagnosis of amnestic MCI with varying levels of depression were examined with the Geriatric Depression Scale (GDS-15), the Functional Rating Scale for Symptoms of Dementia (FRSSD), and the Legal Capacity for Property Law Transactions Assessment Scale (LCPLTAS). Cusp catastrophe analysis was applied to the data, which suggested that the nonlinear model was superior to the linear and logistic alternatives, demonstrating depression contributes to a bifurcation effect. Depressive symptomatology induces nonlinear effects, that is, beyond a threshold value sudden decline in financial capacity is observed. Implications for theory and practice are discussed.

Neural Synchrony and Network Dynamics in Social Interaction: A Hyper-Brain Cell Assembly Hypothesis

Mounting neurophysiological evidence suggests that interpersonal interaction relies on continual communication between cell assemblies within interacting brains and continual adjustments of these neuronal dynamic states between the brains. In this Hypothesis and Theory article, a Hyper-Brain Cell Assembly Hypothesis is suggested on the basis of a conceptual review of neural synchrony and network dynamics and their roles in emerging cell assemblies within the interacting brains. The proposed hypothesis states that such cell assemblies can emerge not only within, but also between the interacting brains. More precisely, the hyper-brain cell assembly encompasses and integrates oscillatory activity within and between brains, and represents a common hyper-brain unit, which has a certain relation to social behavior and interaction. Hyper-brain modules or communities, comprising nodes across two or several brains, are considered as one of the possible representations of the hypothesized hyper-brain cell assemblies, which can also have a multidimensional or multilayer structure. It is concluded that the neuronal dynamics during interpersonal interaction is brain-wide, i.e., it is based on common neuronal activity of several brains or, more generally, of the coupled physiological systems including brains.

Affect-Logic, Embodiment, Synergetics, and the Free Energy Principle: New Approaches to the Understanding and Treatment of Schizophrenia

This theoretical paper explores the affect-logic approach to schizophrenia in light of the general complexity theories of cognition: embodied cognition, Haken's synergetics, and Friston's free energy principle. According to affect-logic, the mental apparatus is an embodied system open to its environment, driven by bioenergetic inputs of emotions. Emotions are rooted in goal-directed embodied states selected by evolutionary pressure for coping with specific situations such as fight, flight, attachment, and others. According to synergetics, nonlinear bifurcations and the emergence of new global patterns occur in open systems when control parameters reach a critical level. Applied to the emergence of psychotic states, synergetics and the proposed energetic understanding of emotions lead to the hypothesis that critical levels of emotional tension may be responsible for the transition from normal to psychotic modes of functioning in vulnerable individuals. In addition, the free energy principle through learning suggests that psychotic symptoms correspond to alternative modes of minimizing free energy, which then entails distorted perceptions of the body, self, and reality. This synthetic formulation has implications for novel therapeutic and preventive strategies in the treatment of psychoses, among these are milieu-therapeutic approaches of the Soteria type that focus on a sustained reduction of emotional tension and phenomenologically oriented methods for improving the perception of body, self, and reality.

Beyond Dyadic Coupling: The Method of Multivariate Surrogate Synchrony (mv-SUSY)

Measuring interpersonal synchrony is a promising approach to assess the complexity of social interaction, which however has been mostly limited to dyads. In this study, we introduce multivariate Surrogate Synchrony (mv-SUSY) to extend the current set of computational methods. Methods: mv-SUSY was applied to eight datasets consisting of 10 time series each, all with n = 9600 observations. Datasets 1 to 5 consist of simulated time series with the following characteristics: white noise (dataset 1), non-stationarity with linear time trends (dataset 2), autocorrelation (dataset 3), oscillation (dataset 4), and multivariate correlation (dataset 5). Datasets 6 to 8 comprise empirical multivariate movement data of two individuals (datasets 6 and 7) and between members of a group discussion (dataset 8.) Results: As hypothesized, findings of mv-SUSY revealed absence of synchrony in datasets 1 to 4 and presence of synchrony in dataset 5. In the empirical datasets, mv-SUSY indicated significant movement synchrony. These results were predominantly replicated by two well-established dyadic synchrony approaches, Surrogate Synchrony (SUSY) and Surrogate Concordance (SUCO). Conclusions: The study applied and evaluated a novel synchrony approach, mv-SUSY. We demonstrated the feasibility and validity of estimating multivariate nonverbal synchrony within and between individuals by mv-SUSY.