# Larry S. Liebovitch's research while affiliated with CUNY Graduate Center and other places

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## Publications (156)

A comparative anthropological perspective reveals not only that some human societies do not engage in war, but also that peaceful social systems exist. Peace systems are defined as clusters of neighbouring societies that do not make war with each other. The mere existence of peace systems is important because it demonstrates that creating peaceful...

Despite good faith attempts by countless citizens, civil society, governments, and the international community, living in a sustainably peaceful community continues to be an elusive dream in much of our world. Among the challenges to sustaining peace is the fact that few scholars have studied enduringly peaceful societies, or have examined only nar...

Scholarly research on peace has overwhelmingly focused on negative peace, or the absence of conflict, aggression, violence, and war. We seek to understand holistic peace systems, the political, economic, and social systems that sustain peaceful societies. We show how two methods can help us understand the properties and dynamics of such complex pea...

Peace is not merely the absence of war and violence, rather ‘positive peace’ is the political, economic, and social systems that generate and sustain peaceful societies. Our international and multidisciplinary group is using physics inspired complex systems analysis methods to understand the factors and their interactions that together support and...

The recent United Nation Secretary General's report on sustaining peace speaks to an urgent crisis of complexity in global affairs, where a wide assortment of nonstate actors wields more political power than ever before. In this context, the international community's traditional ways of forecasting, planning, policymaking, and assessing impact are...

We present a study of natural language using the recurrence network method. In our approach, the repetition of patterns of characters is evaluated without considering the word structure in written texts from different natural languages. Our dataset comprises 85 ebookseBooks written in 17 different European languages. The similarity between patterns...

Mathematics has been used to describe the assumptions and determine their consequences in the physical sciences over the last three centuries. More recently, mathematics has been used to develop a deeper understanding of complex biological phenomena and data. We are now witnessing the expansion of mathematical methods into the social sciences. In t...

We investigated the evolution of inequality in ancient Maya society using the sizes of houses as a proxy for household wealth. We used several mathematical and statistical methods to study the distribution of wealth at four major archaeological sites in the Maya lowlands: Komchén, Palenque, Sayil, and Mayapán. We calculated the Gini coefficient and...

For decades peace has been studied only in the context of resolving conflicts, aggression, war, and violence. But peace is not just the absence of those negatives. Very little is known about the fundamental conditions needed to create and sustain peace. The AC4 consortium at Columbia University has led an international, cross-disciplinary project t...

In this chapter, we present an extension of the mathematical model of the therapeutic relationship developed by Liebovitch and Peluso by investigating relationship ruptures. We present a simulation work that models a repair to relationship ruptures and investigates its potential impact on the success of the therapy. This new model suggests that an...

New methods of computational modeling and new areas of their application will expand the importance of the mathematical modeling of social relationships. To take full advantage, these new methods may require interdisciplinary teams of scientists.

Nash’s equilibrium is one of the most famous and widely used concepts of game theory. It has the ability to predict the best possible outcome based on the strategies of all the participating parties, thereby providing the most beneficial action for all of them to perform. It has been most valuable when applied to ideal conditions. For this reason,...

Residential buildings may be described as complex social-technological systems expressing component interdependence and chaotic temporal variability. As such, we characterized the dynamics and multiscale relationships of hourly electricity consumption data for 13 occupied Florida houses from calendar year 2013. Statistical approaches included: (1)...

We study the correlation properties of word lengths in large texts from 30 ebooks in the English language from the Gutenberg Project (www.gutenberg.org) using the natural visibility graph method (NVG). NVG converts a time series into a graph and then analyzes its graph properties. First, the original sequence of words is transformed into a sequence...

Rationale: A lack of consensus on the conceptualization and definition of peace and the conditions associated with its sustainability has adverse implications for research, policy and practice. This study aims to initiate an interdisciplinary dialogue that can serve to synthetize the core definitions and key elements associated with sustainable pea...

We present a study of the social dynamics among cooperative and competitive actors interacting on a complex network that has a small-world topology. In this model, the state of each actor depends on its previous state in time, its inertia to change, and the influence of its neighboring actors. Using numerical simulations, we determine how the distr...

We studied the behavioral and emotional dynamics displayed by two people trying to resolve a conflict. 59 groups of two people were asked to talk for 20 minutes to try to reach a consensus about a topic on which they disagreed. The topics were abortion, affirmative action, death penalty, and euthanasia. Behavior data were determined from audio reco...

BOOK JACKET: Conflict is inherent in virtually every aspect of human relations, from sport to parliamentary democracy, from fashion in the arts to paradigmatic challenges in the sciences, and from economic activity to intimate relationships. Yet, it can become among the most serious social problems humans face when it loses its constructive feature...

Does agreement or disagreement alone strongly influence people’s thoughts and emotions, or does cognitive and affective reaction relate more to shifts in agreement and disagreement? The present study investigated how attitudes and emotions respond to the evolution of different patterns of agreement and disagreement in an interaction. Combining conv...

The preceding chapters have established the rationale for reframing the essential features of conflict in terms of the principles, metaphors, and methods of dynamical systems. As emphasized in Chap. 2, however, this reframing would be impossible without the accumulated insights and evidence provided by the study of peace and conflict and by the pri...

This is a book about conflict. But it is also a book about essential features of human nature that are expressed in every type of human interaction. In an even broader sense, this is a book about the basic processes that link conflict to a vast array of phenomena in the physical world. These seem like incompatible agendas. Conflict is not the only...

Although uncommon, when the perfect storm of intractable conflict hits, it can undermine the security and well-being of families, communities, and societies everywhere. When viewed through the lens of dynamical systems, both the low frequency and highly destructive consequences of this perplexing phenomenon become understandable. In general terms,...

Despite the assumption of linear causality embedded in the last 400 years of science, it is almost impossible to predict specific outcomes in any nonlinear social system; their dynamics are too complex. Post-hoc determinations of causality can be made, but these are extremely difficult to ascertain a priori (Jones & Hughes, 2003). However, general...

In Chap. 1 we stated that the focus of this book is on conflict. However, all along we have had a hidden agenda (or latent attractor): as ultimately we seek a better understanding and articulation of peace. Of course, peace is more than the absence of destructive conflict. Attempts to suppress conflict can, in fact, have the ironic effect of promot...

The dynamical systems approach to conflict is relatively new, but it has deep roots in other orientations and research agendas. Particularly noteworthy are three very distinct areas of inquiry with equally distinct historical pedigrees: peace and conflict studies, social psychology, and complexity science. As the John Whiting quote implies, each of...

Conflict is a defining feature of human relations. It would be naïve, if not irresponsible, to think that antagonistic interactions among individuals, groups, and nations can ever be eliminated or marginalized, no matter how much we learn about the root causes of such interactions. A realistic goal is to understand the fundamental dynamics that pro...

Kurt Lewin (1948) famously observed, “there is nothing so practical as a good theory.” This simple statement captures a truism regarding the interplay of understanding, prediction, and control that characterizes every area of science. Predicting how a phenomenon will be manifest under different conditions, let alone controlling the process, is inti...

We present a study of time-delay effects on a two-actor conflict model based on nonlinear differential equations. The state of each actor depends on its own state in isolation, its previous state, its inertia to change, the positive or negative feedback and a time delay in the state of the other actor. We use both theoretical and numerical approach...

We investigated how people’s attitudes and emotions change in a social interaction when the interaction changes from cooperation to conflict or vice versa. In two studies, participants completed an attitude survey before and after communicating with a confederate whose scripted behavior reflected sustained cooperation, sustained conflict, or a chan...

Large molecules such as proteins have many of the properties of neural networks. Hence, neural networks may serve as a natural and thus efficient method to compute the time dependent changes of the structure in large molecules. We describe how to encode the spatial conformation and energy structure of a molecule in a neural network. The dynamics of...

Mathematical models, such as the one developed by Gottman et al. (1998, 2000, 2002) to understand the interaction between husbands and wives, can provide novel insights into the dynamics of the therapeutic relationship. A set of nonlinear equations were used to model the changing emotional state of a therapist and client. The results suggest: (1) T...

The success of psychotherapy depends on the nature of the therapeutic relationship between a therapist and a client. We use dynamical systems theory to model the dynamics of the emotional interaction between a therapist and client. We determine how the therapeutic endpoint and the dynamics of getting there depend on the parameters of the model. Pre...

The PU.1 and GATA1 genes play an important role in the differentiation of blood stem cells. The protein levels expressed by these genes are thought to be regulated by a self-excitatory feedback loop for each gene and a cross-inhibitory feedback loop between the two genes. A mathematical model that captures the dynamical interaction between these tw...

In dynamical systems theory, an attractor is a point to which different trajectories converge upon over time. Dynamical psychology theories use the idea of an attractor as a metaphor for human thought and behavior, including judgments, self-concept, and habits (Nowak & Vallacher, 1998, Dynamical Social Psychology, Guilford). While methods to examin...

Genes influence the expression of each other through a complex, nonlinear, dynamical network of interactions. There are a number of interesting open questions about what kind of information can be determined about the structure and dynamics of this network from limited experimental data.

Nonlinear dynamical systems (NDS) theory offers some markedly different perspectives on chance and determinism in scientific explanations of phenomena, mechanical systems versus complex adaptive system, the concepts of dimensions and complexity, and basic notions of change and equilibria. Its inventory of new concepts for understanding change inclu...

The file contains all 117 subnets used in our study, derived from RegulonDB 6.3. The first gene in each line represents the root node of the respective subnet.
(0.05 MB TXT)

Text S1 contains 7 supplementary figures.
(0.95 MB PDF)

The set of regulatory interactions between genes, mediated by transcription factors, forms a species' transcriptional regulatory network (TRN). By comparing this network with measured gene expression data, one can identify functional properties of the TRN and gain general insight into transcriptional control. We define the subnet of a node as the s...

Sustained resonance in a linear oscillator is achievable with a drive whose constant frequency matches the resonant frequency of the oscillator. But in oscillators with nonlinear restoring forces such as the pendulum, Duffing and Duffing–Van der Pol oscillator, the resonant frequency changes as the amplitude changes, so a constant frequency drive r...

To investigate the evolution of market dynamics in different stages of historical
development, we analyze commodity prices from two distinct periods —ancient Babylon, and
medieval and early modern England. We find that the first-digit distributions of both Babylon
and England commodity prices follow Benford’s law, indicating that the data represent...

A nonlinear mathematical model of the interactions in time between 2 actors (which could be individuals, groups, or nations) based on the theoretical and experimental insights of Deutsch (1973, 2006); Pruitt (1969, 2006); Gottman, Murray, Swanson, Tyson, and Swanson (2002); Gottman, Swanson, and Swanson (2002); and Coleman, Vallacher, Nowak, and Bu...

We present evidence that human hunter-gatherers employ foraging movement patterns that are described by the statistics of
Lévy flights rather than by conventional Gaussian statistics. Human movement across the landscape is not usually considered
an anthropological problem as such. For example, Green (1987, p. 273) observed that the way foragers mov...

A specialized presentation of fractal analysis oriented to the social sciences
Publisher's description:
This primer uses straightforward language to give the reader step-by-step instructions for identifying and analyzing fractal patterns and the social process that create them. By making fractals accessible to the social science students, this bo...

With the cessation of cooperation between groups or individuals comes the threat that temporary competition transforms into destructive intractable conflict. To better understand how intractable conflicts develop, Liebovitch, Naudot, Vallacher, Nowak, Bui-Wrzosinksa, and Coleman (2008, Physica A387: 6360-6378) recently developed a non-linear model...

We found that amiloride and SITS, which are inhibitors of passive movements of Na+ and HCO- across cell membranes, inhibited but did not abolish the electrical potential difference and net fluid transport across the rabbit corneal endothelium.

The expression of genes depends on the physical structure of DNA, how the function of DNA is regulated by the transcription factors expressed by other genes, RNA regulation, such as that through RNA interference, and protein signals mediated by protein-protein interaction networks. We illustrate different approaches to determining information about...

A mathematical model for conflict can give us insight into which mechanisms are the most important in maintaining or resolving a conflict. We developed a nonlinear model of the interactions in time between two groups based on the intuitive and experimental insights of Deustch (1973, 2006) and Pruitt (1969, 2006) and the dynamical insights of Gottma...

The time course of an epidemic can be modeled using the differential equations that describe the spread of disease and by dividing people into “patches” of different sizes with the migration of people between these patches. We used these multi-patch, flux-based models to determine how the time course of infected and susceptible populations depends...

A first passage time distribution (FPTD) based on 3-D hyperbolic dif-fusion addressed to the "ball and chain" model, is presented. The resulting shape of FPTD with respect to time is shown. The possibility for compar-ison with experimental data is also provided.

We analyzed data on Ju/’hoansi hunter–gatherer foraging patterns and found that their movements between residence camps can
be modeled as a Lévy flight. The step lengths of their movements scale as a power law with an exponent μ = 1.97. Their wait times (residence times) at the camps also scale as a power law (μ = 1.45). A Lévy flight with step len...

Drugs designed for a specific target are always found to have multiple effects. Rather than hope that one bullet can be designed to hit only one target, nonlinear interactions across genomic and proteomic networks could be used to design Combinatorial Multi-Component Therapies (CMCT) that are more targeted with fewer side effects. We show here how...

The two goals of Nonlinear Biomedical Physics are: firstly to show how nonlinear methods can shed new light on biological phenomena and medical applications and secondly to bridge the technical, mathematical, and cultural divides between the physical disciplines where these methods are being developed and the audience for their use in the biologica...

Previous studies of genetic interactions have focused on measuring and analyzing the level of mRNA expressed by each gene and then finding statistical correlations between them. Here we focus on assessing the global pattern, not the level of activity of specific genes. We formulate models of different architectures of genetic interactions, includin...

It is a pleasure for me to be here, both to talk and to listen. I thank Curt Lindberg and the other organizers for this opportunity.
It has been a long time since I have been here in Austin. In fact, the last time I came here, from Boston; I got here by flying
on Eastern Airlines. So it’s been some time. What I would like to do is to try to knit to...

DNA is transcribed into mRNA, which is translated into proteins. These proteins can then bind back onto the DNA and increase or decrease gene expression. Nature is a circular dance of positive and negative feedback. Each gene influences the expression of other genes. New methods of analysis are now being developed to discover the nature of this net...

Many archaeological patterns are fractal. Fractal analysis, therefore, has much to contribute to archaeology. This article offers an introduction to fractal analysis for archaeologists. We explain what fractals are, describe the essential methods of fractal analysis, and present archaeological examples. Some examples have been published previously,...

A cell in a biological organism consists of thousands of molecules that are used in various complicated biochemical processes. While a cell performs its individual functions it is also involved with other cells in the overall function of the organism. Therefore, each cell in a biological organism is a component with individual and collective proper...

The expression of some genes increases or decreases the expression of other genes forming a complex network of interactions. Typically, correlations between the expression of different genes under different conditions have been used to identify specific regulatory links between specific genes. Instead of that "bottom up" approach, here we try to id...

Classical disease models use a mass action term as the interaction between infected and susceptible people in separate patches. We derive the equations when this interaction is a migration of people between patches. The results model what happens when a new population is moved into a region with endemic disease.

Analysis of the timing of the arrival of email viruses at different computers provides a way of probing the structural and dynamical properties of the Internet. We found that the intervals t between the arrival of four different strains of email viruses have a power law distribution proportional to t(-d), where 1.5<or=d<or=3.2 and that there are po...

The statistical measures commonly used to assess therapies for recurrent atrial arrhythmias (such as time to first recurrence) often assume a uniformly random pattern of arrhythmic events over time. However, the true temporal pattern of atrial arrhythmia recurrences is unknown. The aim of this study was to use linear and nonlinear analyses to chara...

Ions cross the cell membrane through ion channel proteins. The traditional approaches have analyzed channel proteins as if they existed in a few stable conformations and switched rapidly between them. However, we show here the importance of dynamical properties in these proteins. These properties include continuous internal motions and continuous c...

Most methods used to analyze experimental data are based on the assumption that the data is from a Gaussian distribution and uncorrected. We describe methods to analyze data from scaling phenomena that do not have a Gaussian distribution [8.1–8.3] or involve long-range correlations [8.4–8.6]. We then show how those scaling methods have proved usefu...

We describe the traditional nonfractal and the new fractal methods used to analyze the currents through ion channels in the cell membrane. We discuss the hidden assumptions used in these methods and how those assumptions lead to different interpretations of the same experimental data. The nonfractal methods assumed that channel proteins have a smal...

The gating of ion channels has been modeled by assuming that the transitions between open and closed states is a memoryless process. Nevertheless, analysis of records of unitary current events suggests that the kinetic process presents short-term memory, i.e. the open- and closed-dwell times are short-term correlated. Here the rescaled range analys...

We used to think that a good measurement is characterized by its mean and variance and that a good theory is characterized by its ability to predict the values measured in an experiment. The properties of nonlinear systems called fractals and chaos have now taught us that this isn't necessarily true. Data from fractal systems extend over many scale...

Fractal behavior has been observed in both ion-channel gating and neuronal spiking patterns, but a causal relationship between the two has not yet been established. Here, we examine the effects of fractal ion-channel activity in modifications of two classical neuronal models: Fitzhugh-Nagumo (FHN) and Hodgkin-Huxley (HH). For the modified FHN model...

We show that the feedback from the macroscopic dynamics of a system of coupled units can synchronize the dynamics of these units. We studied the dynamics of maps coupled through their variables and control parameters. The feedback adjusted the values of the parameters of each map by using a function that depended on the difference between the Liapu...

A reversible, internal adsorption of cations was picked as one of the possible reasons of nonlinear behaviour of ionic transport through single channel in a membrane. The power law scaling in an adsorption term of the overall discrete dynamical equation for current provides an opportunity for implementing the structure–function relationship. The lo...

We show how one dynamical system can be used to control another dynamical system or coupled set of systems. We do this by having the parameters of the target system depend on the difference of Liapunov exponents between the control and target systems. This is illustrated with logistic and Chirikov maps. A single system can stabilize a target system...