90 research outputs found
The Role of Noise in the Spatial Public Goods Game
In this work we aim to analyze the role of noise in the spatial Public Goods
Game, one of the most famous games in Evolutionary Game Theory. The dynamics of
this game is affected by a number of parameters and processes, namely the
topology of interactions among the agents, the synergy factor, and the strategy
revision phase. The latter is a process that allows agents to change their
strategy. Notably, rational agents tend to imitate richer neighbors, in order
to increase the probability to maximize their payoff. By implementing a
stochastic revision process, it is possible to control the level of noise in
the system, so that even irrational updates may occur. In particular, in this
work we study the effect of noise on the macroscopic behavior of a finite
structured population playing the Public Goods Game. We consider both the case
of a homogeneous population, where the noise in the system is controlled by
tuning a parameter representing the level of stochasticity in the strategy
revision phase, and a heterogeneous population composed of a variable
proportion of rational and irrational agents. In both cases numerical
investigations show that the Public Goods Game has a very rich behavior which
strongly depends on the amount of noise in the system and on the value of the
synergy factor. To conclude, our study sheds a new light on the relations
between the microscopic dynamics of the Public Goods Game and its macroscopic
behavior, strengthening the link between the field of Evolutionary Game Theory
and statistical physics.Comment: 14 pages, 3 figure
Success and luck in creative careers
Luck is considered to be a crucial ingredient to achieve impact in all
creative domains, despite their diversity. For instance, in science, the movie
industry, music, and art, the occurrence of the highest impact work and of a
hot streak within a creative career are very difficult to predict. Are there
domains that are more prone to luck than others? Here, we provide new insights
on the role of randomness in impact in creative careers in two ways: (i) we
systematically untangle luck and individual ability to generate impact in the
movie, music, and book industries, and in science, and compare the luck factor
between these fields; (ii) we show the limited predictive power of
collaboration networks to predict career hits. Taken together, our analysis
suggests that luck consistently affects career impact across all considered
sectors and improves our understanding in pinpointing the key elements in the
prediction of success
An Information Theoretic approach to Post Randomization Methods under Differential Privacy
Post Randomization Methods (PRAM) are among the most popular disclosure limitation techniques for both categorical and continuous data. In the categorical case, given a stochastic matrix M and a specified variable, an individual belonging to category i is changed to category j with probability Mi,j . Every approach to choose the randomization matrix M has to balance between two desiderata: 1) preserving as much statistical information from the raw data as possible; 2) guaranteeing the privacy of individuals in the dataset. This trade-off has generally been shown to be very challenging to solve. In this work, we use recent tools from the computer science literature and propose to choose M as the solution of a constrained maximization problems. Specifically, M is chosen as the solution of a constrained maximization problem, where we maximize the Mutual Information between raw and transformed data, given the constraint that the transformation satisfies the notion of Differential Privacy. For the general Categorical model, it is shown how this maximization problem reduces to a convex linear programming and can be therefore solved with known optimization algorithms
Quantifying human performance in chess
From sports to science, the recent availability of large-scale data has
allowed to gain insights on the drivers of human innovation and success in a
variety of domains. Here we quantify human performance in the popular game of
chess by leveraging a very large dataset comprising of over 120 million games
between almost 1 million players. We find that individuals encounter hot
streaks of repeated success, longer for beginners than for expert players, and
even longer cold streaks of unsatisfying performance. Skilled players can be
distinguished from the others based on their gaming behaviour. Differences
appear from the very first moves of the game, with experts tending to
specialize and repeat the same openings while beginners explore and diversify
more. However, experts experience a broader response repertoire, and display a
deeper understanding of different variations within the same line. Over time,
the opening diversity of a player tends to decrease, hinting at the development
of individual playing styles. Nevertheless, we find that players are often not
able to recognize their most successful openings. Overall, our work contributes
to quantifying human performance in competitive settings, providing a first
large-scale quantitative analysis of individual careers in chess, helping
unveil the determinants separating elite from beginner performance.Comment: 8 pages, 5 figure
Multiorder Laplacian for synchronization in higher-order networks
Traditionally, interaction systems have been described as networks, where
links encode information on the pairwise influences among the nodes. Yet, in
many systems, interactions take place in larger groups. Recent work has shown
that higher-order interactions between oscillators can significantly affect
synchronization. However, these early studies have mostly considered
interactions up to 4 oscillators at time, and analytical treatments are limited
to the all-to-all setting. Here, we propose a general framework that allows us
to effectively study populations of oscillators where higher-order interactions
of all possible orders are considered, for any complex topology described by
arbitrary hypergraphs, and for general coupling functions. To this scope, we
introduce a multi-order Laplacian whose spectrum determines the stability of
the synchronized solution. Our framework is validated on three structures of
interactions of increasing complexity. First, we study a population with
all-to-all interactions at all orders, for which we can derive in a full
analytical manner the Lyapunov exponents of the system, and for which we
investigate the effect of including attractive and repulsive interactions.
Second, we apply the multi-order Laplacian framework to synchronization on a
synthetic model with heterogeneous higher-order interactions. Finally, we
compare the dynamics of coupled oscillators with higher-order and pairwise
couplings only, for a real dataset describing the macaque brain connectome,
highlighting the importance of faithfully representing the complexity of
interactions in real-world systems. Taken together, our multi-order Laplacian
allows us to obtain a complete analytical characterization of the stability of
synchrony in arbitrary higher-order networks, paving the way towards a general
treatment of dynamical processes beyond pairwise interactions.Comment: Was "A multi-order Laplacian framework for the stability of
higher-order synchronization
The structure and dynamics of multiplex networks
PhDNetwork science has provided useful answers to research questions in many fields, from
biology to social science, from ecology to urban science. The first analyses of networked
systems focused on binary networks, where only the topology of the connections were
considered. Soon network scientists started considering weighted networks, to represent
interactions with different strength, cost, or distance in space and time. Also, connections
are not fixed but change over time. This is why in more recent years, a lot of attention
has been devoted to temporal or time-varying networks.
We now entered the era of multi-layer networks, or multiplex networks, relational systems
whose units are connected by different relationships, with links of distinct types
embedded in different layers. Multiplexity has been observed in many contexts, from
social network analysis to economics, medicine and ecology. The new challenge consists
in applying the new tools of multiplex theory to unveil the richness associated to this
novel level of complexity. How do agents organise their interactions across layers? How
does this affect the dynamics of the system?
In the first part of the thesis, we provide a mathematical framework to deal with multiplex
networks. We suggest metrics to unveil multiplexity from basic node, layer and edge
properties to more complicated structure at the micro- and meso-scale, such as motifs,
communities and cores. Measures are validated through the analysis of real-world systems
such as social and collaboration networks, transportation systems and the human
brain.
In the second part of the thesis we focus on dynamical processes taking place on top of
multiplex networks, namely biased random walks, opinion dynamics, cultural dynamics
and evolutionary game theory. All these examples show how multiplexity is crucial to
determine the emergence of unexpected and instrinsically multiplex collective behavior,
opening novel perspectives for the field of non-linear dynamics on networks.European Union project LASAGN
Do higher-order interactions promote synchronization?
Understanding how nonpairwise interactions alter dynamical processes in
networks is of fundamental importance to the characterization and control of
many coupled systems. Recent discoveries of hyperedge-enhanced synchronization
under various settings raised speculations that such enhancements might be a
general phenomenon. Here, we demonstrate that even for simple systems such as
Kuramoto oscillators, the effects of higher-order interactions are highly
representation-dependent. Specifically, we show numerically and analytically
that hyperedges typically enhance synchronization in random hypergraphs, but
have the opposite effect in simplicial complexes. As an explanation, we
identify higher-order degree heterogeneity as the key structural determinant of
synchronization stability in systems with a fixed coupling budget. Our findings
highlight the importance of appropriate representations in describing
higher-order interactions. In particular, the choice of simplicial complexes or
hypergraphs has significant ramifications and should not be purely motivated by
technical conveniences.Comment: Comments welcome! Y.Z. and M.L. contributed equally to this work.
Code available at https://github.com/maximelucas/higherorder_sync_promote
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