arXiv subjects

G. Korniss

Publications and source records attributed to G. Korniss.

At least 19 recordsLinked to original sources

arXiv2024

Fluctuations and Persistence in Quantum Diffusion on Regular Lattices

We investigate quantum persistence by analyzing amplitude and phase fluctuations of the wave function governed by the time-dependent free-particle Schrödinger equation. The quantum system is initialized with local random uncorrelated Gaussian amplitude and phase fluctuations. In analogy with classical diffusion, the persistence probability is defined as the probability that the local (amplitude or phase) fluctuations have not changed sign up to time $t$. Our results show that the persistence probability in quantum diffusion exhibits exponential-like tails. More specifically, in $d=1$ the persistence probability decays in a stretched exponential fashion, while in $d=2$ and $d=3$ as an exponential. We also provide some insights by analyzing the two-point spatial and temporal correlation functions in the limit of small fluctuations. In particular, in the long-time limit, the temporal correlation functions for both local amplitude and phase fluctuations become time-homogeneous, i.e., the zero-crossing events correspond to those of a stationary Gaussian process, with sufficiently fast-decaying power-law tail of its autocorrelation function, implying an exponential-like tail of the persistence probabilities.

cond-mat.stat-mech↗

arXiv2017

The Investigation of Social Media Data Thresholds for Opinion Formation

The pervasive use of social media has grown to over two billion users to date, and is commonly utilized as a means to share information and shape world events. Evidence suggests that passive social media usage (i.e., viewing without taking action) has an impact on the user's perspective. This empirical influence over perspective could have significant impact on social events. Therefore, it is important to understand how social media contributes to the formation of an individual's perspective. A set of experimental tasks were designed to investigate empirically derived thresholds for opinion formation as a result of passive interactions with different social media data types (i.e., videos, images, and messages). With a better understanding of how humans passively interact with social media information, a paradigm can be developed that allows the exploitation of this interaction and plays a significant role in future military plans and operations.

cs.SI↗

arXiv2016

Assortative Mating: Encounter-Network Topology and the Evolution of Attractiveness

We model a social-encounter network where linked nodes match for reproduction in a manner depending probabilistically on each node`s attractiveness. The developed model reveals that increasing either the network`s mean degree or the ``choosiness`` exercised during pair-formation increases the strength of positive assortative mating. That is, we note that attractiveness is correlated among mated nodes. Their total number also increases with mean degree and selectivity during pair-formation. By iterating over model mapping of parents onto offspring across generations, we study the evolution of attractiveness. Selection mediated by exclusion from reproduction increases mean attractiveness, but is rapidly balanced by skew in the offspring distribution of highly attractive mated pairs.

physics.soc-ph↗

arXiv2016

Competing Effects of Social Balance and Influence

We study a three-state (leftist, rightist, centrist) model that couples the dynamics of social balance with an external deradicalizing field. The mean-field analysis shows that there exists a critical value of the external field $p_c$ such that for a weak external field ($p$$<$$p_c$), the system exhibits a metastable fixed point and a saddle point in addition to a stable fixed point. However, if the strength of the external field is sufficiently large ($p$$>$$p_c$), there is only one (stable) fixed point which corresponds to an all-centrist consensus state (absorbing state). In the weak-field regime, the convergence time to the absorbing state is evaluated using the quasi-stationary distribution and is found to be in agreement with the results obtained by numerical simulations.

physics.soc-ph↗

arXiv2015

Social consensus and tipping points with opinion inertia

When opinions, behaviors or ideas diffuse within a population, some are invariably stickier than others. The stickier the opinion, behavior or idea, the greater is an individual's inertia to replace it with an alternative. Here we study the effect of stickiness of opinions in a two-opinion model, where individuals change their opinion only after a certain number of consecutive encounters with the alternative opinion. Assuming that one opinion has a fixed stickiness, we investigate how the critical size of the competing opinion required to tip over the entire population varies as a function of the competing opinion's stickiness. We analyze this scenario for the case of a complete-graph topology through simulations, and through a semi-analytical approach which yields an upper bound for the critical minority size. We present analogous simulation results for the case of the Erdős-Rényi random network. Finally, we investigate the coarsening properties of sticky opinion spreading on two-dimensional lattices, and show that the presence of stickiness gives rise to an effective surface tension that causes the coarsening behavior to become curvature-driven.

physics.soc-ph↗

arXiv2015

Extreme Fluctuations in Stochastic Network Coordination with Time Delays

We study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks. We obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network. We then obtain the scaling behavior of the extreme fluctuations with system size, as well as the distribution of the extremes on complex networks, and compare them to those on regular one-dimensional lattices. For large complex networks, when the delay is not too close to the critical one, fluctuations at the nodes effectively decouple, and the limit distributions converge to the Fisher-Tippett-Gumbel density. In contrast, fluctuations in low-dimensional spatial graphs are strongly correlated, and the limit distribution of the extremes is the Airy density. Finally, we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes.

cond-mat.stat-mech↗

arXiv2014

Building Damage-Resilient Dominating Sets in Complex Networks against Random and Targeted Attacks

We study the vulnerability of dominating sets against random and targeted node removals in complex networks. While small, cost-efficient dominating sets play a significant role in controllability and observability of these networks, a fixed and intact network structure is always implicitly assumed. We find that cost-efficiency of dominating sets optimized for small size alone comes at a price of being vulnerable to damage; domination in the remaining network can be severely disrupted, even if a small fraction of dominator nodes are lost. We develop two new methods for finding flexible dominating sets, allowing either adjustable overall resilience, or dominating set size, while maximizing the dominated fraction of the remaining network after the attack. We analyze the efficiency of each method on synthetic scale-free networks, as well as real complex networks.

physics.soc-ph↗

arXiv2014

Opinion Dynamics and Influencing on Random Geometric Graphs

We investigate the two-word Naming Game on two-dimensional random geometric graphs. Studying this model advances our understanding of the spatial distribution and propagation of opinions in social dynamics. A main feature of this model is the spontaneous emergence of spatial structures called opinion domains which are geographic regions with clear boundaries within which all individuals share the same opinion. We provide the mean-field equation for the underlying dynamics and discuss several properties of the equation such as the stationary solutions and two-time-scale separation. For the evolution of the opinion domains we find that the opinion domain boundary propagates at a speed proportional to its curvature. Finally we investigate the impact of committed agents on opinion domains and find the scaling of consensus time.

math.DS↗

arXiv2014

Dominating Scale-Free Networks Using Generalized Probabilistic Methods

We study ensemble-based graph-theoretical methods aiming to approximate the size of the minimum dominating set (MDS) in scale-free networks. We analyze both analytical upper bounds of dominating sets and numerical realizations for applications. We propose two novel probabilistic dominating set selection strategies that are applicable to heterogeneous networks. One of them obtains the smallest probabilistic dominating set and also outperforms the deterministic degree-ranked method. We show that a degree-dependent probabilistic selection method becomes optimal in its deterministic limit. In addition, we also find the precise limit where selecting high-degree nodes exclusively becomes inefficient for network domination. We validate our results on several real-world networks, and provide highly accurate analytical estimates for our methods.

physics.soc-ph↗

arXiv2014

Dispersal limitation and roughening of the ecological interface

Limited dispersal distance, whether associated with vegetative growth or localized reproduction, induces spatial clustering and, in turn, focuses ecological interactions at the neighborhood scale. In particular, most invasive plants are clonal, cluster through vegetative propagation, and compete locally. Dispersal limitation implies that invasive spread occurs as advance of an ecological interface between invader and resident species. Interspecific competition along the interface produces random variation in the extent of invasive growth. Development of these random fluctuations, termed stochastic roughening, will often structure the interface as a self-affine fractal; a series of power-law scaling relationships follows as a result. For a diverse array of local growth processes exhibiting both forward and lateral propagation, the extent of invader advance becomes spatially correlated along the interface, and the width of the interface (the area where invader and resident compete directly) increases as a power function of time. Once roughening equilibrates statistically, interface width and the location of the most advanced invader (the "front-runner") beyond the mean incursion should both increase as a power function of interface length. To test these predictions, we let white clover (Trifolium repens) invade ryegrass (Lolium perenne) experimentally. Spatial correlation developed as anticipated, and both interface width and the front-runner's lead scaled as a power law of length. However, the scaling exponents differed, likely a consequence of clover's growth morphology. The theory of kinetic roughening offers a new framework for understanding causes and consequences of spatial pattern in between-species interaction, and indicates when interface measures at a local scale predict properties of an invasive front at extended spatial scales.

q-bio.PE↗

arXiv2013

Minimum Dominating Sets in Scale-Free Network Ensembles

We study the scaling behavior of the size of minimum dominating set (MDS) in scale-free networks, with respect to network size $N$ and power-law exponent $γ$, while keeping the average degree fixed. We study ensembles generated by three different network construction methods, and we use a greedy algorithm to approximate the MDS. With a structural cutoff imposed on the maximal degree ($k_{\max}=\sqrt{N}$) we find linear scaling of the MDS size with respect to $N$ in all three network classes. Without any cutoff ($k_{\max}=N-1$) two of the network classes display a transition at $γ\approx 1.9$, with linear scaling above, and vanishingly weak dependence below, but in the third network class we find linear scaling irrespective of $γ$. We find that the partial MDS, which dominates a given $z<1$ fraction of nodes, displays essentially the same scaling behavior as the MDS.

physics.soc-ph↗

arXiv2013

Threshold-limited spreading in social networks with multiple initiators

A classical model for social-influence-driven opinion change is the threshold model. Here we study cascades of opinion change driven by threshold model dynamics in the case where multiple {\it initiators} trigger the cascade, and where all nodes possess the same adoption threshold $ϕ$. Specifically, using empirical and stylized models of social networks, we study cascade size as a function of the initiator fraction $p$. We find that even for arbitrarily high value of $ϕ$, there exists a critical initiator fraction $p_c(ϕ)$ beyond which the cascade becomes global. Network structure, in particular clustering, plays a significant role in this scenario. Similarly to the case of single-node or single-clique initiators studied previously, we observe that community structure within the network facilitates opinion spread to a larger extent than a homogeneous random network. Finally, we study the efficacy of different initiator selection strategies on the size of the cascade and the cascade window.

physics.soc-ph↗

arXiv2013

Restoration Ecology: Two-Sex Dynamics and Cost Minimization

We model a spatially detailed, two-sex population dynamics, to study the cost of ecological restoration. We assume that cost is proportional to the number of individuals introduced into a large habitat. We treat dispersal as homogeneous diffusion. The local population dynamics depends on sex ratio at birth, and allows mortality rates to differ between sexes. Furthermore, local density dependence induces a strong Allee effect, implying that the initial population must be sufficiently large to avert rapid extinction. We address three different initial spatial distributions for the introduced individuals; for each we minimize the associated cost, constrained by the requirement that the species must be restored throughout the habitat. First, we consider spatially inhomogeneous, unstable stationary solutions of the model's equations as plausible candidates for small restoration cost. Second, we use numerical simulations to find the smallest cluster size, enclosing a spatially homogeneous population density, that minimizes the cost of assured restoration. Finally, by employing simulated annealing, we minimize restoration cost among all possible initial spatial distributions of females and males. For biased sex ratios, or for a significant between-sex difference in mortality, we find that sex-specific spatial distributions minimize the cost. But as long as the sex ratio maximizes the local equilibrium density for given mortality rates, a common homogeneous distribution for both sexes that spans a critical distance yields a similarly low cost.

q-bio.PE↗

arXiv2012

Network Coordination and Synchronization in a Noisy Environment with Time Delays

We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in complex networks. We consider two types of time delays: transmission delays between interacting nodes and local delays at each node (due to processing, cognitive, or execution delays). By investigating the underlying fluctuations for several delay schemes, we obtain the synchronizability threshold (phase boundary) and the scaling behavior of the width of the synchronization landscape, in some cases for arbitrary networks and in others for specific weighted networks. Numerical computations allow the behavior of these networks to be explored when direct analytical results are not available. We comment on the implications of these findings for simple locally or globally weighted network couplings and possible trade-offs present in such systems.

cond-mat.stat-mech↗

arXiv2012

Extraordinary Sex Ratios: Cultural Effects on Ecological Consequences

We model sex-structured population dynamics to analyze pairwise competition between groups differing both genetically and culturally. A sex-ratio allele is expressed in the heterogametic sex only, so that assumptions of Fisher's analysis do not apply. Sex-ratio evolution drives cultural evolution of a group-associated trait governing mortality in the homogametic sex. The two-sex dynamics under resource limitation induces a strong Allee effect that depends on both sex ratio and cultural trait values. We describe the resulting threshold, separating extinction from positive growth, as a function of female and male densities. When initial conditions avoid extinction due to the Allee effect, different sex ratios cannot coexist; in our model, greater female allocation always invades and excludes a lesser allocation. But the culturally transmitted trait interacts with the sex ratio to determine the ecological consequences of successful invasion. The invading female allocation may permit population persistence at self-regulated equilibrium. For this case, the resident culture may be excluded, or may coexist with the invader culture. That is, a single sex-ratio allele in females and a cultural dimorphism in male mortality can persist; a low-mortality resident trait is maintained by father-to-son cultural transmission. Otherwise, the successfully invading female allocation excludes the resident allele and culture, and then drives the population to extinction via a shortage of males. Finally, we show that the results obtained under homogeneous mixing hold, with caveats, in a spatially explicit model with local mating and diffusive dispersal in both sexes.

q-bio.PE↗

arXiv2012

Evolution of opinions on social networks in the presence of competing committed groups

Public opinion is often affected by the presence of committed groups of individuals dedicated to competing points of view. Using a model of pairwise social influence, we study how the presence of such groups within social networks affects the outcome and the speed of evolution of the overall opinion on the network. Earlier work indicated that a single committed group within a dense social network can cause the entire network to quickly adopt the group's opinion (in times scaling logarithmically with the network size), so long as the committed group constitutes more than about 10% of the population (with the findings being qualitatively similar for sparse networks as well). Here we study the more general case of opinion evolution when two groups committed to distinct, competing opinions $A$ and $B$, and constituting fractions $p_A$ and $p_B$ of the total population respectively, are present in the network. We show for stylized social networks (including Erdős-Rényi random graphs and Barabási-Albert scale-free networks) that the phase diagram of this system in parameter space $(p_A,p_B)$ consists of two regions, one where two stable steady-states coexist, and the remaining where only a single stable steady-state exists. These two regions are separated by two fold-bifurcation (spinodal) lines which meet tangentially and terminate at a cusp (critical point). We provide further insights to the phase diagram and to the nature of the underlying phase transitions by investigating the model on infinite (mean-field limit), finite complete graphs and finite sparse networks. For the latter case, we also derive the scaling exponent associated with the exponential growth of switching times as a function of the distance from the critical point.

physics.soc-ph↗

arXiv2011

Distributed flow optimization and cascading effects in weighted complex networks

We investigate the effect of a specific edge weighting scheme $\sim (k_i k_j)^β$ on distributed flow efficiency and robustness to cascading failures in scale-free networks. In particular, we analyze a simple, yet fundamental distributed flow model: current flow in random resistor networks. By the tuning of control parameter $β$ and by considering two general cases of relative node processing capabilities as well as the effect of bandwidth, we show the dependence of transport efficiency upon the correlations between the topology and weights. By studying the severity of cascades for different control parameter $β$, we find that network resilience to cascading overloads and network throughput is optimal for the same value of $β$ over the range of node capacities and available bandwidth.

physics.soc-ph↗

arXiv2011

Accelerating consensus on co-evolving networks: the effect of committed individuals

Social networks are not static but rather constantly evolve in time. One of the elements thought to drive the evolution of social network structure is homophily - the need for individuals to connect with others who are similar to them. In this paper, we study how the spread of a new opinion, idea, or behavior on such a homophily-driven social network is affected by the changing network structure. In particular, using simulations, we study a variant of the Axelrod model on a network with a homophilic rewiring rule imposed. First, we find that the presence of homophilic rewiring within the network, in general, impedes the reaching of consensus in opinion, as the time to reach consensus diverges exponentially with network size $N$. We then investigate whether the introduction of committed individuals who are rigid in their opinion on a particular issue, can speed up the convergence to consensus on that issue. We demonstrate that as committed agents are added, beyond a critical value of the committed fraction, the consensus time growth becomes logarithmic in network size $N$. Furthermore, we show that slight changes in the interaction rule can produce strikingly different results in the scaling behavior of $T_c$. However, the benefit gained by introducing committed agents is qualitatively preserved across all the interaction rules we consider.

physics.soc-ph↗