arXiv subjects

Julien Randon-Furling

Publications and source records attributed to Julien Randon-Furling.

At least 19 recordsLinked to original sources

arXiv2026

Uncovering Social Network Activity Using Joint User and Topic Interaction

The emergence of online social platforms, such as social networks and social media, has drastically affected the way people apprehend the information flows to which they are exposed. In such platforms, various information cascades spreading among users is the main force creating complex dynamics of opinion formation, each user being characterized by their own behavior adoption mechanism. Moreover, the spread of multiple pieces of information or beliefs in a networked population is rarely uncorrelated. In this paper, we introduce the Mixture of Interacting Cascades (MIC), a model of marked multidimensional Hawkes processes with the capacity to model jointly non-trivial interaction between cascades and users. We emphasize on the interplay between information cascades and user activity, and use a mixture of temporal point processes to build a coupled user/cascade point process model. Experiments on synthetic and real data highlight the benefits of this approach and demonstrate that MIC achieves superior performance to existing methods in modeling the spread of information cascades. Finally, we demonstrate how MIC can provide, through its learned parameters, insightful bi-layered visualizations of real social network activity data.

cs.SI↗

arXiv2026

Aligning the Unseen in Attributed Graphs: Interplay between Graph Geometry and Node Attributes Manifold

The standard approach to representation learning on attributed graphs -- i.e., simultaneously reconstructing node attributes and graph structure -- is geometrically flawed, as it merges two potentially incompatible metric spaces. This forces a destructive alignment that erodes information about the graph's underlying generative process. To recover this lost signal, we introduce a custom variational autoencoder that separates manifold learning from structural alignment. By quantifying the metric distortion needed to map the attribute manifold onto the graph's Heat Kernel, we transform geometric conflict into an interpretable structural descriptor. Experiments show our method uncovers connectivity patterns and anomalies undetectable by conventional approaches, proving both their theoretical inadequacy and practical limitations.

cs.AI↗

arXiv2025

On the transmission of texts: written cultures as complex systems

Our knowledge of past cultures relies considerably on written material. For centuries, texts have been copied, altered, then transmitted or lost - eventually, from surviving documents, philologists attempt to reconstruct text phylogenies ("stemmata"), and past written cultures. Nonetheless, fundamental questions on the extent of losses, representativeness of surviving artefacts, and the dynamics of text genealogies have remained open since the earliest days of philology. To address these, we radically rethink the study of text transmission through a complexity science approach, integrating stochastic modelling, computer simulations, and data analysis, in a parsimonious mindset akin to statistical physics and evolutionary biology. Thus, we design models that are simple and general, while accounting for diachrony and other key aspects of the dynamical process underlying text phylogenies, such as the extinction of entire branches or trees. On the well-known case study of Medieval French chivalric literature, we find that up to 60% of texts and 99% of manuscripts were lost (consistent with recent synchronic "biodiversity" analyses). We also settle a hundred-year-old controversy on the bifidity of stemmata. Further, our null model suggests that pure chance ("drift") is not the only mechanism at play, and we provide a theoretical and empirical framework for future investigation.

physics.soc-ph↗

arXiv2022

Lost Manuscripts and Extinct Texts: A Dynamic Model of Cultural Transmission

How did written works evolve, disappear or survive down through the ages? In this paper, we propose a unified, formal framework for two fundamental questions in the study of the transmission of texts: how much was lost or preserved from all works of the past, and why do their genealogies (their ``phylogenetic trees'') present the very peculiar shapes that we observe or, more precisely, reconstruct? We argue here that these questions share similarities to those encountered in evolutionary biology, and can be described in terms of ``genetic'' drift and ``natural'' selection. Through agent-based models, we show that such properties as have been observed by philologists since the 1800s can be simulated, and confronted to data gathered for ancient and medieval texts across Europe, in order to obtain plausible estimations of the number of works and manuscripts that existed and were lost.

q-bio.PE↗

arXiv2021

On a first hit distribution of the running maximum of Brownian motion

Let $(S_t)_{t\geq 0}$ be the running maximum of a standard Brownian motion $(B_t)_{t\geq 0}$ and $T_m:=\inf\{t; \, mS_t 0$. In this note we calculate the joint distribution of $T_m$ and $B_{T_m}$. The motivation for our work comes from a mathematical model for animal foraging. We also present results for Brownian motion with drift.

math.PR↗

arXiv2020

Convex hulls of several multidimensional Gaussian random walks

We derive explicit formulae for the expected volume and the expected number of facets of the convex hull of several multidimensional Gaussian random walks in terms of the Gaussian persistence probabilities. Special cases include the already known results about the convex hull of a single Gaussian random walk and the $d$-dimensional Gaussian polytope with or without the origin.

math.PR↗

arXiv2018

From Urban Segregation to Spatial Pattern Detection

We develop a "multifocal" approach to reveal spatial dissimilarities in cities, from the most local scale to the metropolitan one. Think for instance of a statistical variable that may be measured at different scales, eg ethnic group proportions, social housing rate, income distribution, or public transportation network density. Then, to any point in the city there corresponds a sequence of values for the variable, as one zooms out around the starting point, all the way up to the whole city -- as if with a varifocal camera lens. The sequences thus produced encode in a precise manner spatial dissimilarities: how much they differ from perfectly random sequences is indeed a signature of the underlying spatial structure. We introduce here a mathematical framework that allows to analyze this signature and we provide a number of illustrative examples.

physics.soc-ph↗

arXiv2018

Multidimensional Urban Segregation - Toward A Neural Network Measure

We introduce a multidimensional, neural-network approach to reveal and measure urban segregation phenomena, based on the Self-Organizing Map algorithm (SOM). The multidimensionality of SOM allows one to apprehend a large number of variables simultaneously, defined on census or other types of statistical blocks, and to perform clustering along them. Levels of segregation are then measured through correlations between distances on the neural network and distances on the actual geographical map. Further, the stochasticity of SOM enables one to quantify levels of heterogeneity across census blocks. We illustrate this new method on data available for the city of Paris.

physics.soc-ph↗

arXiv2017

A network model for the propagation of Hepatitis C with HIV co-infection

We define and examine a model of epidemic propagation for a virus such as Hepatitis C (with HIV co-infection) on a network of networks, namely the network of French urban areas. One network level is that of the individual interactions inside each urban area. The second level is that of the areas themselves, linked by individuals travelling between these areas and potentially helping the epidemic spread from one city to another. We choose to encode the second level of the network as extra, special nodes in the first level. We observe that such an encoding leads to sensible results in terms of the extent and speed of propagation of an epidemic, depending on its source point.

physics.soc-ph↗

arXiv2017

Facets on the convex hull of $d$-dimensional Brownian and Lévy motion

For stationary, homogeneous Markov processes (viz., Lévy processes, including Brownian motion) in dimension $d\geq 3$, we establish an exact formula for the average number of $(d-1)$-dimensional facets that can be defined by $d$ points on the process's path. This formula defines a universality class in that it is independent of the increments' distribution, and it admits a closed form when $d=3$, a case which is of particular interest for applications in biophysics, chemistry and polymer science. We also show that the asymptotical average number of facets behaves as $\langle \mathcal{F}_T^{(d)}\rangle \sim 2\left[\ln \left( T/Δt\right)\right]^{d-1}$, where $T$ is the total duration of the motion and $Δt$ is the minimum time lapse separating points that define a facet.

cond-mat.stat-mech↗

arXiv2015

From Markovian to non-Markovian persistence exponents

We establish an exact formula relating the survival probability for certain Lévy flights (viz. asymmetric $α$-stable processes where $α= 1/2$) with the survival probability for the order statistics of the running maxima of two independent Brownian particles. This formula allows us to show that the persistence exponent $δ$ in the latter, non Markovian case is simply related to the persistence exponent $θ$ in the former, Markovian case via: $δ=θ/2$. Thus, our formula reveals a link between two recently explored families of anomalous exponents: one exhibiting continuous deviations from Sparre-Andersen universality in a Markovian context, and one describing the slow kinetics of the non Markovian process corresponding to the difference between two independent Brownian maxima.

cond-mat.stat-mech↗

arXiv2014

Universality and time-scale invariance for the shape of planar Lévy processes

For a broad class of planar Markov processes, viz. Lévy processes satisfying certain conditions (valid \textit{eg} in the case of Brownian motion and Lévy flights), we establish an exact, universal formula describing the shape of the convex hull of sample paths. We show indeed that the average number of edges joining paths' points separated by a time-lapse $Δτ\in \left[Δτ_1, Δτ_2\right]$ is equal to $2\ln \left(Δτ_2 / Δτ_1 \right)$, regardless of the specific distribution of the process's increments and regardless of its total duration $T$. The formula also exhibits invariance when the time scale is multiplied by any constant. Apart from its theoretical importance, our result provides new insights regarding the shape of two-dimensional objects modelled by stochastic processes' sample paths (\textit{eg} polymer chains): in particular for a total time (or parameter) duration $T$, the average number of edges on the convex hull ("cut off" to discard edges joining points separated by a time-lapse shorter than some $Δτ< T$) will be given by $2 \ln \left(\frac{T}{Δτ}\right)$. Thus it will only grow logarithmically, rather than at some higher pace.

cond-mat.stat-mech↗

arXiv2013

A Schelling model with switching agents: decreasing segregation via random allocation and social mobility

We study the behaviour of a Schelling-class system in which a fraction $f$ of spatially-fixed switching agents is introduced. This new model allows for multiple interpretations, including: (i) random, non-preferential allocation (\textit{e.g.} by housing associations) of given, fixed sites in an open residential system, and (ii) superimposition of social and spatial mobility in a closed residential system.\\ We find that the presence of switching agents in a segregative Schelling-type dynamics can lead to the emergence of intermediate patterns (\textit{e.g.} mixture of patches, fuzzy interfaces) as the ones described in Ref. 1. We also investigate different transitions between segregated and mixed phases both at $f=0$ and along lines of increasing $f$, where the nature of the transition changes.

cond-mat.stat-mech↗

arXiv2012

Convex hull of n planar Brownian paths: an exact formula for the average number of edges

We establish an exact formula for the average number of edges appearing on the boundary of the global convex hull of n independent Brownian paths in the plane. This requires the introduction of a counting criterion which amounts to "cutting off" edges that are, in a specific sense, small. The main argument consists in a mapping between planar Brownian convex hulls and configurations of constrained, independent linear Brownian motions. This new formula is confirmed by retrieving an existing exact result on the average perimeter of the boundary of Brownian convex hulls in the plane.

cond-mat.stat-mech↗

arXiv2009

Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].

cond-mat.stat-mech↗

arXiv2009

Convex Hull of N Planar Brownian Motions: Exact Results and an Application to Ecology

We compute exactly the mean perimeter and area of the convex hull of N independent planar Brownian paths each of duration T, both for open and closed paths. We show that the mean perimeter < L_N > = α_N, \sqrt{T} and the mean area = β_N T for all T. The prefactors α_N and β_N, computed exactly for all N, increase very slowly (logarithmically) with increasing N. This slow growth is a consequence of extreme value statistics and has interesting implication in ecological context in estimating the home range of a herd of animals with population size N.

cond-mat.stat-mech↗

arXiv2008

Exact distribution of the maximal height of p vicious walkers

Using path integral techniques, we compute exactly the distribution of the maximal height H_p of p nonintersecting Brownian walkers over a unit time interval in one dimension, both for excursions (p-watermelons with a wall) and bridges (p-watermelons without a wall), for all integer p\ge 1. For large p, we show that < H_p > \sim \sqrt{2p} (excursions) whereas < H_p > \sim \sqrt{p} (bridges). Our exact results prove that previous numerical experiments only measured the pre-asymptotic behaviors and not the correct asymptotic ones. In addition, our method establishes a physical connection between vicious walkers and random matrix theory.

cond-mat.stat-mech↗

arXiv2008

Distribution of the time at which the deviation of a Brownian motion is maximum before its first-passage time

We calculate analytically the probability density $P(t_m)$ of the time $t_m$ at which a continuous-time Brownian motion (with and without drift) attains its maximum before passing through the origin for the first time. We also compute the joint probability density $P(M,t_m)$ of the maximum $M$ and $t_m$. In the driftless case, we find that $P(t_m)$ has power-law tails: $P(t_m)\sim t_m^{-3/2}$ for large $t_m$ and $P(t_m)\sim t_m^{-1/2}$ for small $t_m$. In presence of a drift towards the origin, $P(t_m)$ decays exponentially for large $t_m$. The results from numerical simulations are in excellent agreement with our analytical predictions.

cond-mat.stat-mech↗