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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: 24 pages, 15 figures; added references

Understanding how the complex connectivity structure of the brain shapes its information-processing capabilities is a long-standing question. Here, 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 information is maximized at the edge of stability, where excitation is balanced by inhibition. When the input switches among different stimuli, this maximum corresponds to the entropy of the external switching dynamics. By analyzing the case of a prolonged stimulus, we find that stronger inhibition is 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 open the avenue for a complete information-theoretic understanding of how and why inhibition strength should be tuned to optimize information-processing capabilities.

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.

Signatures of photo-induced superconductivity have been reported in cuprate materials subjected to a coherent phonon drive. A 'cold' superfluid was extracted from the transient Terahertz conductivity and was seen to coexist with 'hot' uncondensed quasi-particles, a hallmark of a driven-dissipative system of which the interplay between coherent and incoherent responses are not well understood. Here, time resolved spontaneous Raman scattering was used to probe the lattice temperature in the photo-induced superconducting state of YBa2Cu3O6.48. An increase in lattice temperature of approximately 80 K was observed by measuring the time dependent Raman scattering intensity of an undriven 'spectator' phonon mode. This is to be compared with an estimated increase in quasi-particle temperatures of nearly 200 K. These temperature changes provide quantitative information on the nature of the driven state and its decay, and may provide a strategy to optimize this effect., Comment: 14 pages, 4 figures

Recently, there has been much progress in understanding stationary measures for colored (also called multi-species or multi-type) interacting particle systems, motivated by asymptotic phenomena and rich underlying algebraic and combinatorial structures (such as nonsymmetric Macdonald polynomials). In this paper, we present a unified approach to constructing stationary measures for most of the known colored particle systems on the ring and the line, including (1) the Asymmetric Simple Exclusion Process (multispecies ASEP, or mASEP); (2) the q-deformed Totally Asymmetric Zero Range Process (TAZRP) also known as the q-Boson particle system; (3) the q-deformed Pushing Totally Asymmetric Simple Exclusion Process (q-PushTASEP). Our method is based on integrable stochastic vertex models and the Yang-Baxter equation. We express the stationary measures as partition functions of new "queue vertex models" on the cylinder. The stationarity property is a direct consequence of the Yang-Baxter equation. For the mASEP on the ring, a particular case of our vertex model is equivalent to the multiline queues of Martin (arXiv:1810.10650). For the colored q-Boson process and the q-PushTASEP on the ring, we recover and generalize known stationary measures constructed using multiline queues or other methods by Ayyer-Mandelshtam-Martin (arXiv:2011.06117, arXiv:2209.09859), and Bukh-Cox (arXiv:1912.03510). Our proofs of stationarity use the Yang-Baxter equation and bypass the Matrix Product Ansatz used for the mASEP by Prolhac-Evans-Mallick (arXiv:0812.3293). On the line and in a quadrant, we use the Yang-Baxter equation to establish a general colored Burke's theorem, which implies that suitable specializations of our queue vertex models produce stationary measures for particle systems on the line. We also compute the colored particle currents in stationarity., Comment: 69 pages, 35 figures

We survey the connections between the six-vertex (square ice) model of 2d statistical mechanics and random matrix theory. We highlight the same universal probability distributions appearing on both sides, and also indicate related open questions and conjectures. We present full proofs of two asymptotic theorems for the six-vertex model: in the first one the Gaussian Unitary Ensemble and GUE-corners process appear; the second one leads to the Tracy-Widom distribution $F_2$. While both results are not new, we found shorter transparent proofs for this text. On our way we introduce the key tools in the study of the six-vertex model, including the Yang-Baxter equation and the Izergin-Korepin formula., Comment: 53 pages, v3: fixed typos and made minor edits to improve clarity. To appear in Bulletin of the American Mathematical Society

Critical infrastructure systems - for which high reliability and availability are paramount - must operate securely. Attack trees (ATs) are hierarchical diagrams that offer a flexible modelling language used to assess how systems can be attacked. ATs are widely employed both in industry and academia but - in spite of their popularity - little work has been done to give practitioners instruments to formulate queries on ATs in an understandable yet powerful way. In this paper we fill this gap by presenting ATM, a logic to express quantitative security properties on ATs. ATM allows for the specification of properties involved with security metrics that include "cost", "probability" and "skill" and permits the formulation of insightful what-if scenarios. To showcase its potential, we apply ATM to the case study of a CubeSAT, presenting three different ways in which an attacker can compromise its availability. We showcase property specification on the corresponding attack tree and we present theory and algorithms - based on binary decision diagrams - to check properties and compute metrics of ATM-formulae.

In the manuscript arXiv:2306.07869v1, N. L. Wang and co-authors report the results of a near-infrared pump / terahertz probe study in the stripe-ordered cuprate La$_{1.875}$Ba$_{0.125}$CuO$_4$. They measured a change in optical conductivity, but did not find signatures of transient superconductivity. From this observation they extrapolate that in all cuprates in which striped states have been excited with light, there must be no light-induced superconductivity. They conclude that "transient superconductivity cannot be induced by melting of the competing stripe orders with pump pulses whose photon energy is much higher than the superconducting gap of cuprates." Here we show that this extrapolation is unwarranted. First, the absence of light-induced superconductivity in this particular compound was already reported in a previous paper, which instead showed positive evidence for La$_{1.885}$Ba$_{0.115}$CuO$_4$. In addition, the experiment discussed here used photo-excitation with too low fluence and at a suboptimal wavelength. More broadly, a negative result in one compound is rarely compelling indication of the absence of an effect in an entire class of materials., Comment: 3 pages, 2 figures, comment on arXiv:2306.07869v1

The work of this thesis concerns the problem of linear low energy excitations of vector spin glass models. An analytical and numerical study is carried out, considering a fully connected random-field Heisenberg model at zero temperature, a fully-connected vector p-spin glass model and a sparse random-field Heisenberg model. We test these models against the low temperature behavior of finite dimensional glassy systems, in particular we show that they posses phases where the density of states is gapless with quasi-localised modes. In the case of the sparse model, we show that the density of states follows a quartic law at low frequency, consistently with several recent measures of this quantity that can be found in the literature of computer glasses. In all the three models, the spin glass transition is characterised in terms of the behavior of the softest excitations. We found that in the fully connected models the zero temperature spin glass transition in a field is a delocalisation transition of the softest modes. In the sparse case, a weaker form of delocalisation appears at the transition. These results broaden our understanding of the zero temperature critical point, by showing how spin glass ordering affects the way the system responds to small magnetic perturbations., Comment: PhD thesis