Adam Landsberg

An Assimilation Anomaly: Averaging-Induced Reversal of Overall Opinion in Two Interacting Societies

Journal of Artificial Societies and Social Simulation

Assimilation -the tendency for individuals to adjust their opinions to more closely align with th... more Assimilation -the tendency for individuals to adjust their opinions to more closely align with those around them -is one of the central components of computational social-influence and opinion-dynamics models that seek to elucidate how large-scale societal trends can emerge from local social interactions among small groups of individuals. Although assimilation processes have been well studied using increasingly sophisticated assimilative schemes like bounded confidence, nonlinear opinion-averaging methodologies, time-varying social network structures, etc., we show there is a surprising, previously unrecognized phenomenon lurking in even the simplest of assimilation models. We consider here two societies that start out on opposite sides of some opinion spectrum, for instance, one initially very conservative society and the other very liberal. We assume small groups of individuals from these societies can meet and interact, and that during an interaction each person's opinion simply moves closer to the average opinion of the group. One might anticipate that this barebones assimilation process -which involves nothing more than simple numerical averaging of opinions during each encounter -will invariably lead to a steady (and rather uninteresting) convergence of overall opinion among the two societies wherein the initial intersocietal differences are straightforwardly washed away. We show instead that a counterintuitive, large-scale demographic reversal can sometimes emerge -i.e., the two societies can potentially end up swapping their relative positions on the opinion spectrum, with the initially conservative society ending up more liberal, on the whole, than the formerly liberal society. This finding (dubbed an "assimilation anomaly") shows how the process of repeatedly taking simple averages on a local level can induce an overall reversal of average opinion on a global level. Using a heat diffusion model from physics, we reveal the origins of this curious phenomenon. This dynamical effect involving two interacting societies is wholly distinct from other interesting social-influence phenomena described in the opinion-dynamics literature (e.g., polarization, fragmentation, phase transitions, bifurcations, etc.).

Download

Winning strategies: the emergence of base 2 in the game of nim

The Mathematical Gazette, Jun 22, 2022

Download

Transitioning Out of the Coronavirus Lockdown: A Framework for Evaluating Zone-Based Social Distancing

Frontiers in Public Health, Jun 8, 2020

In the face of elevated pandemic risk, canonical epidemiological models imply the need for extrem... more In the face of elevated pandemic risk, canonical epidemiological models imply the need for extreme social distancing over a prolonged period. Alternatively, people could be organized into zones, with more interactions inside their zone than across zones. Zones can deliver significantly lower infection rates, with less social distancing, particularly if combined with simple quarantine rules and contact tracing. This paper provides a framework for understanding and evaluating the implications of zones, quarantines, and other complementary policies.

Download

Duality and Nonlinear Graph Laplacians

arXiv (Cornell University), Jul 28, 2015

We present an iterative algorithm for solving a class of nonlinear Laplacian system of equations ... more We present an iterative algorithm for solving a class of nonlinear Laplacian system of equations in Õ(k 2 m log(kn/ǫ)) iterations, where k is a measure of nonlinearity, n is the number of variables, m is the number of nonzero entries in the graph Laplacian L, ǫ is the solution accuracy and Õ() neglects (non-leading) logarithmic terms. This algorithm is a natural nonlinear extension of the one by of Kelner et. al., which solves a linear Laplacian system of equations in nearly linear time. Unlike the linear case, in the nonlinear case each iteration takes Õ(n) time so the total running time is Õ(k 2 mn log(kn/ǫ)). For sparse graphs where m = O(n) and fixed k this nonlinear algorithm is Õ(n 2 log(n/ǫ)) which is slightly faster than standard methods for solving linear equations, which require approximately O(n 2.38 ) time. Our analysis relies on the construction of a nonlinear "energy function" and a nonlinear extension of the duality analysis of Kelner et. al to the nonlinear case without any explicit references to spectral analysis or electrical flows. These new insights and results provide tools for more general extensions to spectral theory and nonlinear applications.

Download

Linewidth calculation for bare 2D Josephson arrays

Physics Letters, Sep 1, 1997

We study how disorder affects the frequency-locking properties of a bare current-biased rectangul... more We study how disorder affects the frequency-locking properties of a bare current-biased rectangular array of Josephson junctions. Our calculation is based on a simple physical picture wherein elements within each row lock by virtue of spontaneously induced shunt currents through the transverse junctions; no locking occurs between rows. Our analytic formula for the linewidth is in excellent agreement with numerical simulations of the nonlinear circuit equations.

Download

Cofinite Induced Subgraphs of Impartial Combinatorial Games: An Analysis of CIS-Nim

arXiv (Cornell University), 2012

Given an impartial combinatorial game G, we create a class of related games (CIS-G) by specifying... more Given an impartial combinatorial game G, we create a class of related games (CIS-G) by specifying a finite set of positions in G and forbidding players from moving to those positions (leaving all other game rules unchanged). Such modifications amount to taking cofinite induced subgraphs (CIS) of the original game graph. Some recent numerical/heuristic work has suggested that the underlying structure and behavior of such "CISgames" can shed new light on, and bears interesting relationships with, the original games from which they are derived. In this paper we present an analytical treatment of the cofinite induced subgraphs associated with the game of (three-heap) Nim. This constitutes one of the simplest nontrivial cases of a CIS game. Our main finding is that although the structure of the winning strategies in games of CIS-Nim can differ greatly from that of Nim, CIS-Nim games inherit a type of period-two scale invariance from the original game of Nim.

Download

A Study of the Behavior of Systems of Interacting SOC Automata

APS March Meeting Abstracts, Mar 1, 2003

We examine systems of coupled (SOC) sandpile automata, and describe the emergence of statistical ... more

Disorder-Induced Desynchronization in a 2x2 Circular Josephson Junction Array

APS March Meeting Abstracts, Mar 1, 2000

Analytical results are presented which characterize the behavior of a dc-biased, two-dimensional ... more Analytical results are presented which characterize the behavior of a dc-biased, two-dimensional circular array of overdamped Josephson junctions subject to increasing levels of disorder. It is shown that high levels of disorder can abruptly destroy the synchronous functioning of the array. We identify the transition boundary between synchronized and desynchronized behavior, along with the mechanism responsible for the loss of frequency locking. Comparisons with recent results for arrays with rectangular lattice geometries are described. The circular plaquette model represents a 2ϫ2 array consisting of six overdamped ͓i.e., RSJ ͑Ref. 2͔͒ Josephson junctions. A dc bias current I is fed in uniformly from the outside

Download

The emergence of correlations in studies of global economic inter-dependence and contagion

We construct a simple firm-based automata model for global economic inter-dependence of countries... more

Download

Edge correlations in spatial networks

Journal of Complex Networks, Jun 6, 2015

In this paper, we show that many real-world spatial networks—including demographic migration netw... more In this paper, we show that many real-world spatial networks—including demographic migration networks, social networks and human brain networks—possess ‘spatial edge correlations’ that profoundly affect the network’s underlying structure but which go largely undetected by standard network analysis methods. Even methods designed to characterize the spatial attributes like distribution of edge lengths in a network or the costliness of edge lengths (i.e. long-distance edges tend to be more costly in terms of efficiency, energy, price, etc. than shorter edges) miss the presence of spatial edge correlations. We introduce two network measures designed to detect and quantify these edge correlations, and discuss their implications. We show that even highly simplified models that explicitly take account of these edge correlations can achieve dramatic (potentially order-of-magnitude) improvements over standard network models. We demonstrate the utility of this approach by explaining certain anomalies seen in newly available, highresolution human brain networks. The methods introduced here are very general, with potentially broad applicability to spatial networks across diverse branches of network science.

Spatial Symmetries and Geometrical Phases in Classical Dissipative Systems

Modern Physics Letters B, Jan 20, 1993

We describe the emergence of geometrical phases in dissipative systems with continuous spatial sy... more We describe the emergence of geometrical phases in dissipative systems with continuous spatial symmetries. The phase characterizes the spatial shift of a wave pattern that arises as the result of a cyclic adiabatic transport of control parameters of the system. Geometrical phases are calculated for both stationary and propagating wave patterns. Complementary formulations are provided for finite-dimensional and continuum systems. The theory is used to determine the phase shift for a traveling wave front in a standard reaction-diffusion model.

Winning strategies: the emergence of base 2 in the game of nim

The Mathematical Gazette

Many players know that the secret of winning the game of nim (and other “impartial” combinatorial... more Many players know that the secret of winning the game of nim (and other “impartial” combinatorial games) is to write the sizes of the game’s piles in base 2 and then add them together without carry. The proof of this well-known procedure (described below) is both straightforward and convincing. Nonetheless, the procedure still appears magical, as though a rabbit has been pulled out of a hat. Astute students (and frustrated professors) often ask why the winning strategy for such games involves base 2, and not some other base. After all, nothing about the game of nim itself – the game rules, the configuration of the tokens, etc. – provides any hints about the origin of base 2 in this setting. Minimal insight is offered by most published proofs, which themselves tend to either appear almost wizardly in nature (i.e. assume the base-2 method and show that it miraculously solves the problem) or employ combinatorial arguments that supply little abstract intuition (at least to the authors o...

Download

Transitioning Out of the Coronavirus Lockdown: A Framework for Evaluating Zone-Based Social Distancing

Frontiers in Public Health, 2020

In the face of elevated pandemic risk, is it necessary to completely lock down the population, im... more In the face of elevated pandemic risk, is it necessary to completely lock down the population, imposing extreme social distancing? Canonical epidemiological models suggest this may be unavoidable for months at a time, despite the heavy social and human cost of physically isolating people. Alternatively, people could retreat into socially or economically defined defensive zones, with more interactions inside their zone than across zones. Starting from a complete lockdown, zones could facilitate responsible reopening of education, government, and firms, as a well-implemented structure can dramatically slow the diffusion of the disease. This paper provides a framework for understanding and evaluating the effectiveness of zones for social distancing.

Download

A Study of the Behavior of Systems of Interacting SOC Automata

We examine systems of coupled (SOC) sandpile automata, and describe the emergence of statistical ... more

The emergence of temporal correlations in a study of global economic interdependence

Quantitative Finance, 2003

Abstract We develop a simple firm-based automaton model for global economic interdependence of co... more

New types of waves in systems with O(2) symmetry

Physics Letters A, 1993

A number of novel phenomena arising in systems with O(2) symmetry are described. These include pu... more A number of novel phenomena arising in systems with O(2) symmetry are described. These include pulsing traveling waves with either a periodically or quasiperiodically modulated phase velocity, and heteroclinic waves which alter their appearance with time, taking successively the form of pure traveling waves, standing waves and steady states. Chaotic waves can also be present. These states result from the

Linewidth calculation for bare 2D Josephson arrays

Physics Letters A, 1997

We study how disorder affects the frequency-locking properties of a bare current-biased rectangul... more We study how disorder affects the frequency-locking properties of a bare current-biased rectangular array of Josephson junctions. Our calculation is based on a simple physical picture wherein elements within each row lock by virtue of spontaneously induced shunt currents through the transverse junctions; no locking occurs between rows. Our analytic formula for the linewidth is in excellent agreement with numerical simulations of the nonlinear circuit equations.

Download

Spatial Symmetries and Geometrical Phases in Classical Dissipative Systems

Modern Physics Letters B, 1993

We describe the emergence of geometrical phases in dissipative systems with continuous spatial sy... more We describe the emergence of geometrical phases in dissipative systems with continuous spatial symmetries. The phase characterizes the spatial shift of a wave pattern that arises as the result of a cyclic adiabatic transport of control parameters of the system. Geometrical phases are calculated for both stationary and propagating wave patterns. Complementary formulations are provided for finite-dimensional and continuum systems. The theory is used to determine the phase shift for a traveling wave front in a standard reaction-diffusion model.

On the longitudinal librations of Hyperion

Journal of Fixed Point Theory and Applications, 2009

710 North College Blvd, Claremont, CA 91711. On the Longitudinal Librations of Hyperion. The long... more 710 North College Blvd, Claremont, CA 91711. On the Longitudinal Librations of Hyperion. The longitudinal librations of the satellite Hyperion will be studied under the assumption that the spin axis remains perpendicular to the orbit plane. It will be shown that with probability 1 they are unpredictable. (

Download

On the chaotic behavior of the satellite hyperion

Journal of Difference Equations and Applications, 2005

We model the longitudinal librations of Hyperion with a second order nonlinear differential equat... more We model the longitudinal librations of Hyperion with a second order nonlinear differential equation in which the terms of order e or higher, where e is the eccentricity of the satellite&amp;amp;amp;amp;#39;s elliptical orbit, are neglected. With a suitable change of variable we transform the differential equation into an equivalent one that describes the motion of a forced pendulum with a

Uploads

Papers by Adam Landsberg

Log In