C4

Major depressive disorder (MDD) is a heterogeneous mental disorder. International guidelines present overall symptom severity as the key dimension for clinical characterisation. However, additional layers of heterogeneity may reside within severity levels related to how symptoms interact with one-another in a patient, called symptom dynamics. We investigate these individual differences by estimating the proportion of patients that display differences in their symptom dynamics while sharing the same diagnosis and overall symptom severity. We show that examining symptom dynamics provides information about the person-specific psychopathological expression of patients beyond severity levels by revealing how symptoms aggravate each other over time. These results suggest that symptom dynamics may serve as a promising new dimension for clinical characterisation. Areas of opportunity are outlined for the field of precision psychiatry in uncovering disorder evolution patterns (e.g., spontaneous recovery; critical worsening) and the identification of granular treatment effects by moving toward investigations that leverage symptom dynamics as their foundation. Future work aimed at investigating the cascading dynamics underlying depression onset and maintenance using the large-scale (N > 5.5 million) CIPA Study are outlined. 

I will talk about intersection theory over any globally valued field and how it is connected to some model-theoretic problems.

I will describe a non-commutative version of the Zariski topology and explain how to use it to produce a functorial spectrum for all derived rings. If time permits I will give some examples and show how a weak form of Gelfand duality for non-commutative rings can be deduced from this. This work is in collaboration with Simone Murro and Matteo Capoferri.

Networks provide a powerful language to model interacting systems by representing their units as nodes and the interactions between them as links. Interactions can be connotated in several ways, such as binary/weighted, undirected/directed, etc. In the present talk, we focus on the positive/negative connotation - modelling trust/distrust, alliance/enmity, friendship/conflict, etc. - by considering the so-called signed networks. Rooted in the psychological framework of the balance theory, the study of signed networks has found application in fields as different as biology, ecology, economics. Here, we approach it from the perspective of statistical physics by extending the framework of Exponential Random Graph Models to the class of binary un/directed signed networks and employing it to assess the significance of frustrated patterns in real-world networks. As our results reveal, it critically depends on i) the considered system and ii) the employed benchmark. For what concerns binary directed networks, instead, we explore the relationship between frustration and reciprocity and suggest an alternative interpretation of balance in the light of directionality. Finally,  leveraging the ERGMs framework, we propose an unsupervised algorithm to obtain statistically validated projections of bipartite signed networks, according to which any, two nodes sharing a statistically significant number of concordant (discordant) motifs are connected by a positive (negative) edge, and we investigate signed structures at the mesoscopic scale by evaluating the tendency of a configuration to be either `traditionally' or `relaxedly' balanced.

While the brain has long been conceptualized as a network of neurons connected by synapses, attempts to describe the connectome using established models in network science have yielded conflicting outcomes, leaving the architecture of neural networks unresolved. Here, we analyze eight experimentally mapped connectomes, finding that the degree and the strength distribution of the underlying networks cannot be described by random nor scale-free models. Rather, the node degrees and strengths are well approximated by lognormal distributions, whose emergence lacks a mechanistic model in the context of networks. Acknowledging the fact that the brain is a physical network, whose architecture is driven by the spatially extended nature of its neurons, we analytically derive the multiplicative process responsible for the lognormal neuron length distribution, arriving to a series of empirically falsifiable predictions and testable relationships that govern the degree and the strength of individual neurons. The lognormal network characterizing the connectome represents a novel architecture for network science, that bridges critical gaps between neural structure and function, with unique implications for brain dynamics, robustness, and synchronization.

Our Random Walkers Induced temporal Graphs (RWIG) model generates temporal graph sequences based on M independent, random walkers that traverse an underlying graph as a function of time. Co-location of walkers at a given node and time defines an individual-level contact. RWIG is shown to be a realistic model for temporal human contact graphs.   

A key idea is that a random walk on a Markov graph executes the Markov process. Each of the M walkers traverses the same set of nodes (= states in the Markov graph), but with own transition probabilities (in discrete time) or rates (in continuous time). Hence, the Markov transition probability matrix P_j reflects the policy of motion of walker w_j. RWIG is analytically feasible: we derive closed form solutions for the probability distribution of contact graphs.

Usually, human mobility networks are inferred through measurements of timeseries of contacts between individuals. We also discuss this “inverse RWIG problem”, which aims to determine the parameters in RWIG (i.e. the set of probability transfer matrices P₁, P₂, ..., P_M and the initial probability state vectors s₁[0], ...,s_M[0] of walkers w₁,w₂, ...,w_M in discrete time), given a timeseries of contact graphs.

This talk is based on the article:
Almasan, A.-D., Shvydun, S., Scholtes, I. and P. Van Mieghem, 2025, "Generating Temporal Contact Graphs Using Random Walkers", IEEE Transactions on Network Science and Engineering, to appear.

A base-g Niven number is an integer divisible by the sum of its digits in base-g. We show that any sufficiently large integer can be written as the sum of three base-3 Niven numbers, and comment on the extension to other bases. This is an application of the circle method, which we use to count the number of ways an integer can be written as the sum of three integers with fixed, near-average, digit sum. 

A generalisation of Wiles’ famous modularity theorem, the Fontaine-Mazur conjecture, predicts that two dimensional representations of the absolute Galois group of the rationals, with a few specific properties, exactly correspond to those representations coming from classical modular forms. Under some mild hypotheses, this is now a theorem of Kisin. In this talk, I will explain how one can p-adically interpolate the objects on both sides of this correspondence to construct an eigensurface and “trianguline” Galois deformation space, as well as outline a new approach to proving a theorem of Emerton, that these spaces are often isomorphic.