arXiv subjects

Jean-Charles Delvenne

Publications and source records attributed to Jean-Charles Delvenne.

At least 37 records · Page 2Linked to original sources

arXiv2021

Positive semi-definite embedding for dimensionality reduction and out-of-sample extensions

In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding coordinates are the eigenvectors of a positive semi-definite kernel obtained as the solution of an infinite dimensional analogue of a semi-definite program. This embedding is adaptive and non-linear. We discuss this problem both with weak and strong smoothness assumptions about the learned kernel. A main feature of our approach is the existence of an out-of-sample extension formula of the embedding coordinates in both cases. This extrapolation formula yields an extension of the kernel matrix to a data-dependent Mercer kernel function. Our empirical results indicate that this embedding method is more robust with respect to the influence of outliers, compared with a spectral embedding method.

cs.LG↗

arXiv2021

Beyond Thermodynamic Uncertainty Relations: nonlinear response, error-dissipation trade-offs, and speed limits

From a recent geometric generalization of Thermodynamic Uncertainty Relations (TURs) we derive novel upper bounds on the nonlinear response of an observable of an arbitrary system undergoing a change of probabilistic state. Various relaxations of these bounds allow to recover well known bounds such as (strengthenings of) Cramer-Rao's and Pinsker's inequalities. In particular we obtain a master inequality, named Symmetric Response Intensity Relation, which recovers several TURs as particular cases. We employ this set of bounds for three physical applications. First, we derive a trade-off between thermodynamic cost (dissipated free energy) and reliability of systems switching instantly between two states, such as one-bit memories. We derive in particular a lower bound of $2.8 k_BT$ per Shannon bit to write a bit in such a memory, a bound distinct from Landauer's one. Second, we obtain a new family of classic speed limits which provide lower bounds for non-autonomous Markov processes on the time needed to transition between two probabilistic states in terms of a thermodynamic quantity (e.g. non-equilibrium free energy) and a kinetic quantity (e.g. dynamical activity). Third, we provide an upper bound on the nonlinear response of a system based solely on the `complexity' of the system (which we relate to a high entropy and non-uniformity of the probabilities). We find that `complex' models (e.g. with many states) are necessarily fragile to some perturbations, while simple systems are robust, in that they display a low response to arbitrary perturbations.

cond-mat.stat-mech↗

arXiv2021

State aggregations in Markov chains and block models of networks

We consider state-aggregation schemes for Markov chains from an information-theoretic perspective. Specifically, we consider aggregating the states of a Markov chain such that the mutual information of the aggregated states separated by T time steps is maximized. We show that for T = 1 this approach recovers the maximum-likelihood estimator of the degree-corrected stochastic block model as a particular case, thereby enabling us to explain certain features of the likelihood landscape of this popular generative network model from a dynamical lens. We further highlight how we can uncover coherent, long-range dynamical modules for which considering a time-scale T >> 1 is essential, using synthetic flows and real-world ocean currents, where we are able to recover the fundamental features of the surface currents of the oceans.

physics.soc-ph↗

arXiv2021

Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT

We present a general formalism for the construction of thermodynamically consistent stochastic models of non-linear electronic circuits. The devices constituting the circuit can have arbitrary I-V curves and may include tunnel junctions, diodes, and MOS transistors in subthreshold operation, among others. We provide a full analysis of the stochastic non-equilibrium thermodynamics of these models, identifying the relevant thermodynamic potentials, characterizing the different contributions to the irreversible entropy production, and obtaining different fluctuation theorems. Our work provides a realistic framework to study thermodynamics of computing with electronic circuits. We demonstrate this point by constructing a stochastic model of a CMOS inverter. We find that a deterministic analysis is only compatible with the assumption of equilibrium fluctuations, and analyze how the non-equilibrium fluctuations induce deviations from its deterministic transfer function. Finally, building on the CMOS inverter, we propose a full-CMOS design for a probabilistic bit (or binary stochastic neuron) exploiting intrinsic noise.

cond-mat.stat-mech↗

arXiv2021

Network constraints on the mixing patterns of binary node metadata

We consider the network constraints on the bounds of the assortativity coefficient, which measures the tendency of nodes with the same attribute values to be interconnected. The assortativity coefficient is the Pearson's correlation coefficient of node attribute values across network edges and ranges between -1 and 1. We focus here on the assortativity of binary node attributes and show that properties of the network, such as degree distribution and the number of nodes with each attribute value place constraints upon the attainable values of the assortativity coefficient. We explore the assortativity in three different spaces, that is, ensembles of graph configurations and node-attribute assignments that are valid for a given set of network constraints. We provide means for obtaining bounds on the extremal values of assortativity for each of these spaces. Finally, we demonstrate that under certain conditions the network constraints severely limit the maximum and minimum values of assortativity, which may present issues in how we interpret the assortativity coefficient.

cs.SI↗

arXiv2020

Random Multi-Hopper Model. Super-Fast Random Walks on Graphs

We develop a model for a random walker with long-range hops on general graphs. This random multi-hopper jumps from a node to any other node in the graph with a probability that decays as a function of the shortest-path distance between the two nodes. We consider here two decaying functions in the form of the Laplace and Mellin transforms of the shortest-path distances. Remarkably, when the parameters of these transforms approach zero asymptotically, the multi-hopper's hitting times between any two nodes in the graph converge to their minimum possible value, given by the hitting times of a normal random walker on a complete graph. Stated differently, for small parameter values the multi-hopper explores a general graph as fast as possible when compared to a random walker on a full graph. Using computational experiments we show that compared to the normal random walker, the multi-hopper indeed explores graphs with clusters or skewed degree distributions more efficiently for a large parameter range. We provide further computational evidence of the speed-up attained by the random multi-hopper model with respect to the normal random walker by studying deterministic, random and real-world networks.

physics.soc-ph↗

arXiv2020

Severability of mesoscale components and local time scales in dynamical networks

A major goal of dynamical systems theory is the search for simplified descriptions of the dynamics of a large number of interacting states. For overwhelmingly complex dynamical systems, the derivation of a reduced description on the entire dynamics at once is computationally infeasible. Other complex systems are so expansive that despite the continual onslaught of new data only partial information is available. To address this challenge, we define and optimise for a local quality function severability for measuring the dynamical coherency of a set of states over time. The theoretical underpinnings of severability lie in our local adaptation of the Simon-Ando-Fisher time-scale separation theorem, which formalises the intuition of local wells in the Markov landscape of a dynamical process, or the separation between a microscopic and a macroscopic dynamics. Finally, we demonstrate the practical relevance of severability by applying it to examples drawn from power networks, image segmentation, social networks, metabolic networks, and word association.

physics.soc-ph↗

arXiv2020

The anatomy of Reddit: An overview of academic research

Online forums provide rich environments where users may post questions and comments about different topics. Understanding how people behave in online forums may shed light on the fundamental mechanisms by which collective thinking emerges in a group of individuals, but it has also important practical applications, for instance to improve user experience, increase engagement or automatically identify bullying. Importantly, the datasets generated by the activity of the users are often openly available for researchers, in contrast to other sources of data in computational social science. In this survey, we map the main research directions that arose in recent years and focus primarily on the most popular platform, Reddit. We distinguish and categorise research depending on their focus on the posts or on the users, and point to different types of methodologies to extract information from the structure and dynamics of the system. We emphasize the diversity and richness of the research in terms of questions and methods, and suggest future avenues of research.

cs.SI↗

arXiv2020

Modelling structure and predicting dynamics of discussion threads in online boards

Internet boards are platforms for online discussions about a variety of topics. On these boards, individuals may start a new thread on a specific matter, or leave comments in an existing discussion. The resulting collective process leads to the formation of `discussion trees', where nodes represent a post and comments, and an edge represents a `reply-to' relation. The structure of discussion trees has been analysed in previous works, but only from a static perspective. In this paper, we focus on their structural and dynamical properties by modelling their formation as a self-exciting Hawkes process. We first study a Reddit dataset to show that the structure of the trees resemble those produced by a Galton-Watson process with a special root offspring distribution. The dynamical aspect of the model is then used to predict future commenting activity and the final size of a discussion tree. We compare the efficiency of our approach with previous works and show its superiority for the prediction of the dynamics of discussions.

cs.SI↗

arXiv2020

Stochastic and Quantum Thermodynamics of Driven RLC Networks

We develop a general stochastic thermodynamics of RLC electrical networks built on top of a graph-theoretical representation of the dynamics commonly used by engineers. The network is: open, as it contains resistors and current and voltage sources, nonisothermal as resistors may be at different temperatures, and driven, as circuit elements may be subjected to external parametric driving. The proper description of the heat dissipated in each resistor requires care within the white noise idealization as it depends on the network topology. Our theory provides the basis to design circuits-based thermal machines, as we illustrate by designing a refrigerator using a simple driven circuit. We also derive exact results for the low temperature regime in which the quantum nature of the electrical noise must be taken into account. We do so using a semiclassical approach which can be shown to coincide with a fully quantum treatment of linear circuits for which canonical quantization is possible. We use it to generalize the Landauer-Buttiker formula for energy currents to arbitrary time-dependent driving protocols.

quant-ph↗

arXiv2020

Measuring the effect of node aggregation on community detection

Many times the nodes of a complex network, whether deliberately or not, are aggregated for technical, ethical, legal limitations or privacy reasons. A common example is the geographic position: one may uncover communities in a network of places, or of individuals identified with their typical geographical position, and then aggregate these places into larger entities, such as municipalities, thus obtaining another network. The communities found in the networks obtained at various levels of aggregation may exhibit various degrees of similarity, from full alignment to perfect independence. This is akin to the problem of ecological and atomic fallacies in statistics, or to the Modified Areal Unit Problem in geography. We identify the class of community detection algorithms most suitable to cope with node aggregation, and develop an index for aggregability, capturing to which extent the aggregation preserves the community structure. We illustrate its relevance on real-world examples (mobile phone and Twitter reply-to networks). Our main message is that any node-partitioning analysis performed on aggregated networks should be interpreted with caution, as the outcome may be strongly influenced by the level of the aggregation.

physics.soc-ph↗

arXiv2019

Multi-scale Anomaly Detection on Attributed Networks

Many social and economic systems can be represented as attributed networks encoding the relations between entities who are themselves described by different node attributes. Finding anomalies in these systems is crucial for detecting abuses such as credit card frauds, web spams or network intrusions. Intuitively, anomalous nodes are defined as nodes whose attributes differ starkly from the attributes of a certain set of nodes of reference, called the context of the anomaly. While some methods have proposed to spot anomalies locally, globally or within a community context, the problem remain challenging due to the multi-scale composition of real networks and the heterogeneity of node metadata. Here, we propose a principled way to uncover outlier nodes simultaneously with the context with respect to which they are anomalous, at all relevant scales of the network. We characterize anomalous nodes in terms of the concentration retained for each node after smoothing specific signals localized on the vertices of the graph. Besides, we introduce a graph signal processing formulation of the Markov stability framework used in community detection, in order to find the context of anomalies. The performance of our method is assessed on synthetic and real-world attributed networks and shows superior results concerning state of the art algorithms. Finally, we show the scalability of our approach in large networks employing Chebychev polynomial approximations.

cs.SI↗

arXiv2019

Unifying Thermodynamic Uncertainty Relations

We introduce a new technique to bound the fluctuations exhibited by a physical system, based on the Euclidean geometry of the space of observables. Through a simple unifying argument, we derive a sweeping generalization of so-called Thermodynamic Uncertainty Relations (TURs). We not only strengthen the bounds but extend their realm of applicability and in many cases prove their optimality, without resorting to large deviation theory or information-theoretic techniques. In particular, we find the best TUR based on entropy production alone and also derive a novel bound for stationary Markov processes, which surpasses previous known bounds. Our results derive from the non-invariance of the system under a symmetry which can be other than time reversal and thus open a wide new spectrum of applications.

cond-mat.stat-mech↗

arXiv2019

Multiscale dynamical embeddings of complex networks

Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from Control Theory, we propose a time-dependent dynamical similarity measure between nodes, which quantifies the effect a node-input has on the network. This dynamical similarity induces an embedding that can be employed for several analysis tasks. Here we focus on (i)~dimensionality reduction, i.e., projecting nodes onto a low dimensional space that captures dynamic similarity at different time scales, and (ii)~how to exploit our embeddings to uncover functional modules. We exemplify our ideas through case studies focusing on directed networks without strong connectivity, and signed networks. We further highlight how certain ideas from community detection can be generalized and linked to Control Theory, by using the here developed dynamical perspective.

cs.SI↗

arXiv2019

Unsupervised Network Embedding for Graph Visualization, Clustering and Classification

A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation at node/edge or substructure level. However, many real life challenges such as time-varying, multilayer, chemical compounds and brain networks involve analysis of a family of graphs instead of single one opening additional challenges in graph comparison and representation. Traditional approaches for learning representations relies on hand-crafting specialized heuristics to extract meaningful information about the graphs, e.g statistical properties, structural features, etc. as well as engineered graph distances to quantify dissimilarity between networks. In this work we provide an unsupervised approach to learn embedding representation for a collection of graphs so that it can be used in numerous graph mining tasks. By using an unsupervised neural network approach on input graphs, we aim to capture the underlying distribution of the data in order to discriminate between different class of networks. Our method is assessed empirically on synthetic and real life datasets and evaluated in three different tasks: graph clustering, visualization and classification. Results reveal that our method outperforms well known graph distances and graph-kernels in clustering and classification tasks, being highly efficient in runtime.

cs.SI↗

arXiv2018

Rock-Paper-Scissors Random Walks on Temporal Multilayer Networks

We study diffusion on a multilayer network where the contact dynamics between the nodes is governed by a random process and where the waiting time distribution differs for edges from different layers. We study the impact on a random walk of the competition that naturally emerges between the edges of the different layers. In opposition to previous studies which have imposed a priori inter-layer competition, the competition is here induced by the heterogeneity of the activity on the different layers. We first study the precedence relation between different edges and by extension between different layers, and show that it determines biased paths for the walker. We also discuss the emergence of cyclic, rock-paper-scissors random walks, when the precedence between layers is non-transitive. Finally, we numerically show the slowing-down effect due to the competition on a heterogeneous multilayer as the walker is likely to be trapped for a longer time either on a single layer, or on an oriented cycle . Keywords: random walks; multilayer networks; dynamical systems on networks; models of networks; simulations of networks; competition between layers.

physics.soc-ph↗

arXiv2018

Multi-hop assortativities for networks classification

Several social, medical, engineering and biological challenges rely on discovering the functionality of networks from their structure and node metadata, when it is available. For example, in chemoinformatics one might want to detect whether a molecule is toxic based on structure and atomic types, or discover the research field of a scientific collaboration network. Existing techniques rely on counting or measuring structural patterns that are known to show large variations from network to network, such as the number of triangles, or the assortativity of node metadata. We introduce the concept of multi-hop assortativity, that captures the similarity of the nodes situated at the extremities of a randomly selected path of a given length. We show that multi-hop assortativity unifies various existing concepts and offers a versatile family of 'fingerprints' to characterize networks. These fingerprints allow in turn to recover the functionalities of a network, with the help of the machine learning toolbox. Our method is evaluated empirically on established social and chemoinformatic network benchmarks. Results reveal that our assortativity based features are competitive providing highly accurate results often outperforming state of the art methods for the network classification task.

cs.LG↗

arXiv2018

Multiscale mixing patterns in networks

Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks manifesting as a higher tendency of links occurring between people with the same age, race, or political belief. Quantifying the level of assortativity or disassortativity (the preference of linking to nodes with different attributes) can shed light on the factors involved in the formation of links and contagion processes in complex networks. It is common practice to measure the level of assortativity according to the assortativity coefficient, or modularity in the case of discrete-valued metadata. This global value is the average level of assortativity across the network and may not be a representative statistic when mixing patterns are heterogeneous. For example, a social network spanning the globe may exhibit local differences in mixing patterns as a consequence of differences in cultural norms. Here, we introduce an approach to localise this global measure so that we can describe the assortativity, across multiple scales, at the node level. Consequently we are able to capture and qualitatively evaluate the distribution of mixing patterns in the network. We find that for many real-world networks the distribution of assortativity is skewed, overdispersed and multimodal. Our method provides a clearer lens through which we can more closely examine mixing patterns in networks.

cs.SI↗