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Biological and artificial systems encode information through several complex nonlinear operations, making their exact study a formidable challenge. These internal mechanisms often take place across multiple timescales and process external signals to enable functional output responses. In this work, we focus on two widely implemented paradigms: nonlinear summation, where signals are first processed independently and then combined; and nonlinear integration, where they are combined first and then processed. We study a general model where the input signal is propagated to an output unit through a processing layer via nonlinear activation functions. Further, we distinguish between the two cases of fast and slow processing timescales. We demonstrate that integration and fast-processing capabilities systematically enhance input-output mutual information over a wide range of parameters and system sizes, while simultaneously enabling tunable input discrimination. Moreover, we reveal that high-dimensional embeddings and low-dimensional projections emerge naturally as optimal competing strategies. Our results uncover the foundational features of nonlinear information processing with profound implications for both biological and artificial systems.

Recent technological advances in healthcare have led to unprecedented growth in patient data quantity and diversity. While artificial intelligence (AI) models have shown promising results in analyzing individual data modalities, there is increasing recognition that models integrating multiple complementary data sources, so-called multimodal AI, could enhance clinical decision-making. This scoping review examines the landscape of deep learning-based multimodal AI applications across the medical domain, analyzing 432 papers published between 2018 and 2024. We provide an extensive overview of multimodal AI development across different medical disciplines, examining various architectural approaches, fusion strategies, and common application areas. Our analysis reveals that multimodal AI models consistently outperform their unimodal counterparts, with an average improvement of 6.2 percentage points in AUC. However, several challenges persist, including cross-departmental coordination, heterogeneous data characteristics, and incomplete datasets. We critically assess the technical and practical challenges in developing multimodal AI systems and discuss potential strategies for their clinical implementation, including a brief overview of commercially available multimodal AI models for clinical decision-making. Additionally, we identify key factors driving multimodal AI development and propose recommendations to accelerate the field's maturation. This review provides researchers and clinicians with a thorough understanding of the current state, challenges, and future directions of multimodal AI in medicine., Comment: 28 pages

The landscape of cyber threats grows more complex by the day. Advanced Persistent Threats carry out systematic attack campaigns against which cybersecurity practitioners must defend. Examples of such organized attacks are operations Dream Job, Wocao, WannaCry or the SolarWinds Compromise. To evaluate which risks are most threatening, and which campaigns to prioritize against when defending, cybersecurity experts must be equipped with the right toolbox. In particular, they must be able to (a) obtain likelihood values for each attack campaign recorded in the wild and (b) reliably and transparently operationalize these values to carry out quantitative comparisons among campaigns. This will allow security experts to perform quantitatively-informed decision making that is transparent and accountable. In this paper we construct such a framework by: (1) quantifying the likelihood of attack campaigns via data-driven procedures on the MITRE knowledge base and (2) introducing a methodology for automatic modelling of MITRE intelligence data: this is complete in the sense that it captures any attack campaign via template attack tree models. (3) We further propose a computational framework to carry out this comparisons based on the cATM formal logic, and implement this into an open-source Python tool. Finally, we validate our approach by quantifying the likelihood of all MITRE campaigns, and comparing the likelihood of the Wocao and Dream Job MITRE campaigns -- generated with our proposed approach -- against "ad hoc" traditionally-built attack tree models, demonstrating how our methodology is substantially lighter in modelling effort, and still capable of capturing all the quantitative relevant data.

Real-world systems are shaped by both their complex internal interactions and the changes in their noisy environments. In this work, we study how a shared active bath affects the statistical dependencies between two interacting Brownian particles by evaluating their mutual information. We decompose the mutual information into three terms: information stemming from the internal interactions between the particles; information induced by the shared bath, which encodes environmental changes; a term describing information interference that quantifies how the combined presence of both internal interactions and environment either masks (destructive interference) or boosts (constructive interference) information. By studying exactly the case of linear interactions, we find that the sign of information interference depends solely on that of the internal coupling. However, when internal interactions are described by a nonlinear activation function, we show that both constructive and destructive interference appear depending on the interplay between the timescale of the active environment, the internal interactions, and the environmental coupling. Finally, we show that our results generalize to hierarchical systems where asymmetric couplings to the environment mimic the scenario where the active bath is only partially accessible to one particle. This setting allows us to quantify how this asymmetry drives information interference. Our work underscores how information and functional relationships in complex multi-scale systems are fundamentally shaped by the environmental context.

We study numerically the Hessian of low-lying minima of vector spin glass models defined on random regular graphs. We consider the two-component (XY) and three-component (Heisenberg) spin glasses at zero temperature, subjected to the action of a randomly oriented external field. Varying the intensity of the external field, these models undergo a zero temperature phase transition from a paramagnet at high field to a spin glass at low field. We study how the spectral properties of the Hessian depend on the magnetic field. In particular, we study the shape of the spectrum at low frequency and the localization properties of low energy eigenvectors across the transition. We find that in both phases the edge of the spectral density behaves as $\lambda^{3/2}$: such a behavior rules out the presence of a diverging spin-glass susceptibility $\chi_{SG}=\langle 1/\lambda^2 \rangle$. As to low energy eigenvectors, we find that the softest eigenmodes are always localized in both phases of the two models. However, by studying in detail the geometry of low energy eigenmodes across different energy scales close to the lower edge of the spectrum, we find a different behavior for the two models at the transition: in the XY case, low energy modes are typically localized; at variance, in the Heisenberg case low-energy eigenmodes with a multi-modal structure (sort of ``delocalization'') appear at an energy scale that vanishes in the infinite size limit. These geometrically non-trivial excitations, which we call Concentrated and Delocalised Low Energy Modes (CDLEM), coexist with trivially localised excitations: we interpret their existence as a sign of critical behavior related to the onset of the spin glass phase., Comment: 15 pages, 8 figures

We construct perfect t-embeddings for regular hexagons of the hexagonal lattice, providing the first example, and hence proving existence, for graphs with an outer face of degree greater than four. The construction is in terms of the inverse Kasteleyn matrix and relies only on symmetries of the graph. Using known formulas for the inverse Kasteleyn matrix, we derive exact contour integral formulas for these embeddings and their origami maps. Through steepest descent analysis, we establish scaling limits, proving convergence of origami maps to a maximal surface in the Minkowski space $\mathbb{R}^{2,1}$, and we verify structural rigidity conditions, leading to a new proof of convergence of height fluctuations to the Gaussian free field., Comment: 43 pages, 9 figures

Piezoelectricity, the generation of electric charge in response to mechanical stress, is a key property in both natural and synthetic materials. This study significantly boosts the piezoelectric response of chitosan, a biodegradable biopolymer, by integrating chitin/chitosan nanocrystals into natural chitosan-based thin film elastomers. The resulting materials achieve d$_{33}$ values of 15-19 pmV$^{-1}$, a marked improvement over the 5-9 pmV$^{-1}$ observed in pure chitosan films thanks to increased crystallinity from the nanocrystals. We utilize piezoresponse force microscopy (PFM) to accurately measure the d$_{33}$ coefficient, employing an engineered extraction method that eliminates the electrostatic contribution, which can overestimate the piezoelectric response. The resulting chitosan elastomers exhibit elastic deformation up to 40\% strain and a Young's modulus of approximately 100 MPa, similar to soft tissues. These properties, along with the fact that the employed materials can be entirely crafted from upcycled biowaste, make these elastomers ideal for prosthetics, wearable devices, energy harvesters, and sustainable transducers. Our findings underscore the potential of chitosan-based piezoelectric materials for advanced applications in biotechnology, soft robotics, and the green Internet of Things.

How to distribute a set of points uniformly on a spherical surface is a very old problem that still lacks a definite answer. In this work, we introduce a physical measure of uniformity based on the distribution of distances between points, as an alternative to commonly adopted measures based on interaction potentials. We then use this new measure of uniformity to characterize several algorithms available in the literature. We also study the effect of optimizing the position of the points through the minimization of different interaction potentials via a gradient descent procedure. In this way, we can classify different algorithms and interaction potentials to find the one that generates the most uniform distribution of points on the sphere., Comment: 17 pages, 15 figures

Developing new methods for predicting electromagnetic instabilities in cardiac activity is of primary importance. However, we still need a comprehensive view of the heart's magnetic activity at the tissue scale. To fill this gap, we present a model of soft active matter, including thermo-electric coupling, suitably modified to reproduce cardiac magnetic field. Our theoretical framework shows that periodic stimulations of cardiac cells create an external magnetic field evidencing restitution features of nonlinear cardiac dynamics and magnetic restitution curves better discriminate instabilities and bifurcations in cardiac activity. This new framework lays the foundation for innovative, non-invasive diagnostic tools for cardiac arrhythmias.

Results regarding spin glass models are, to this day, mainly confined to models with Ising spins. Spin glass models with continuous spins exhibit interesting new physical behaviors related to the additional degrees of freedom, but have been primarily studied on fully connected topologies. Only recently some advancements have been made in the study of continuous models on sparse graphs. In this work we partially fill this void by introducing a method to solve numerically the Belief Propagation equations for systems of Heisenberg spins on sparse random graphs via a discretization of the sphere. We introduce techniques to study the finite-temperature, finite-connectivity case as well as novel algorithms to deal with the zero-temperature and large connectivity limits. As an application, we locate the de Almeida-Thouless line for this class of models and the critical field at zero temperature, showing the full consistency of the methods presented. Beyond the specific results reported for Heisenberg models, the approaches presented in this paper have a much broader scope of application and pave the way to the solution of strongly disordered models with continuous variables., Comment: 28 pages, 15 figures; added references

Understanding how the complex connectivity structure of the brain shapes its information-processing capabilities is a long-standing question. By focusing on a paradigmatic architecture, we study how the neural activity of excitatory and inhibitory populations encodes information on external signals. We show that at long times information is maximized at the edge of stability, where inhibition balances excitation, both in linear and nonlinear regimes. In the presence of multiple external signals, this maximum corresponds to the entropy of the input dynamics. By analyzing the case of a prolonged stimulus, we find that stronger inhibition is instead needed to maximize the instantaneous sensitivity, revealing an intrinsic trade-off between short-time responses and long-time accuracy. In agreement with recent experimental findings, our results pave the way for a deeper information-theoretic understanding of how the balance between excitation and inhibitions controls optimal information-processing in neural populations.

Complex systems with multiple processes evolving on different temporal scales are naturally described by multilayer networks, where each layer represents a different timescale. In this work, we show how the multilayer structure shapes the generation and propagation of information between layers. We derive a general decomposition of the multilayer probability for continuous stochastic processes described by Fokker-Planck operators. In particular, we focus on Gaussian processes, for which this solution can be obtained analytically. By explicitly computing the mutual information between the layers, we derive the fundamental principles that govern how information is propagated by the topology of the multilayer network. In particular, we unravel how edges between nodes in different layers affect their functional couplings. We find that interactions from fast to slow layers alone do not generate information, leaving the layers statistically independent even if they affect their dynamical evolution. On the other hand, interactions from slow to fast nodes lead to non-zero mutual information, which can then be propagated along specific paths of interactions between layers. We employ our results to study the interplay between information and instability, identifying the critical layers that drive information when pushed to the edge of stability. Our work generalizes previous results obtained in the context of discrete stochastic processes, allowing us to understand how the multilayer nature of complex systems affects their functional structure.

Metapopulation models have been instrumental in demonstrating the ecological impact of landscape structure on the survival of a focal species in complex environments. However, extensions to multiple species with arbitrary dispersal networks often rely on phenomenological assumptions limiting their scope. Here, we develop a multilayer network model of competitive dispersing metacommunities to investigate how spatially structured environments impact species coexistence and ecosystem stability. We show that homogeneous environments always lead to monodominance unless all species' fitness parameters are in an exact trade-off. However, this precise fine-tuning does not guarantee coexistence in generic heterogeneous environments. By introducing general spatial disorder in the model, we solve it exactly in the mean-field limit, finding that stable coexistence becomes possible in the presence of strong disorder. Crucially, coexistence is supported by the spontaneous localization of species through the emergence of ecological niches. Our results remain qualitatively valid in arbitrary dispersal networks, where topological features can improve species coexistence. Finally, we employ our model to study how correlated disorder promotes spatial ecological patterns in realistic terrestrial and riverine landscapes. Our work provides a novel framework to understand how landscape structure enables coexistence in metacommunities by acting as the substrate for ecological interactions., Comment: 11 pages, 4 figures

Biological and living organisms sense and process information from their surroundings, typically having access only to a subset of external observables for a limited amount of time. In this work, we uncover how biological systems can exploit these accessible degrees of freedom (DOFs) to transduce information from the inaccessible ones with a limited energy budget. We find that optimal transduction strategies may boost information harvesting over the ideal case in which all DOFs are known, even when only finite-time trajectories are observed, at the price of higher dissipation. We apply our results to red blood cells, inferring the implemented transduction strategy from membrane flickering data and shedding light on the connection between mechanical stress and transduction efficiency. Our framework offers novel insights into the adaptive strategies of biological systems under non-equilibrium conditions.

We provide an overview of three different query languages whose objective is to specify properties on the highly popular formalisms of fault trees (FTs) and attack trees (ATs). These are BFL, a Boolean Logic for FTs, PFL, a probabilistic extension of BFL and ATM, a logic for security metrics on ATs. We validate the framework composed by these three logics by applying them to the case study of a water distribution network. We extend the FT for this network - found in the literature - and we propose to model the system under analysis with the Fault Trees/Attack Trees (FT/ATs) formalism, combining both FTs and ATs in a unique model. Furthermore, we propose a novel combination of the showcased logics to account for queries that jointly consider both the FT and the AT of the model, integrating influences of attacks on failure probabilities of different components. Finally, we extend the domain specific language for PFL with novel constructs to capture the interplay between metrics of attacks - e.g., "cost", success probabilities - and failure probabilities in the system.

The pursue of what are properties that can be identified to permit an automated reasoning program to generate and find new and interesting theorems is an interesting research goal (pun intended). The automatic discovery of new theorems is a goal in itself, and it has been addressed in specific areas, with different methods. The separation of the "weeds", uninteresting, trivial facts, from the "wheat", new and interesting facts, is much harder, but is also being addressed by different authors using different approaches. In this paper we will focus on geometry. We present and discuss different approaches for the automatic discovery of geometric theorems (and properties), and different metrics to find the interesting theorems among all those that were generated. After this description we will introduce the first result of this article: an undecidability result proving that having an algorithmic procedure that decides for every possible Turing Machine that produces theorems, whether it is able to produce also interesting theorems, is an undecidable problem. Consequently, we will argue that judging whether a theorem prover is able to produce interesting theorems remains a non deterministic task, at best a task to be addressed by program based in an algorithm guided by heuristics criteria. Therefore, as a human, to satisfy this task two things are necessary: an expert survey that sheds light on what a theorem prover/finder of interesting geometric theorems is, and - to enable this analysis - other surveys that clarify metrics and approaches related to the interestingness of geometric theorems. In the conclusion of this article we will introduce the structure of two of these surveys - the second result of this article - and we will discuss some future work., Comment: In Proceedings ADG 2023, arXiv:2401.10725

Complex systems are characterized by multiple spatial and temporal scales. A natural framework to capture their multiscale nature is that of multilayer networks, where different layers represent distinct physical processes that often regulate each other indirectly. We model these regulatory mechanisms through triadic higher-order interactions between nodes and edges. In this work, we focus on how the different timescales associated with each layer impact their effective couplings in terms of their mutual information. We unravel the general principles governing how such information propagates across the multiscale structure, and apply them to study archetypal examples of biological signaling networks and effective environmental dependencies in stochastic processes. Our framework generalizes to any dynamics on multilayer networks, paving the way for a deeper understanding of how the multiscale nature of real-world systems shapes their information content and complexity.