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A recent paper (ref. 1) used infrared images of Io acquired by the Juno/JIRAM instrument to derive a latitudinal dependence of the spectral radiance and conclude that such latitudinal dependence is consistent with a magma ocean model. We challenge their conclusions, and we draw attention to some potential issues with their analysis. In this letter, we will use three arguments to show that: (1) the (ref. 1) paper uses saturated data; (2) the M-filter of the JIRAM imager is only a weak and incomplete proxy for the total power output; and finally (3) even assuming that the radiance was correctly estimated, the latitudinal dependence of the 4.8-$\mu$m spectral radiance is not statistically significant. These facts, taken together, demonstrate that the results presented in (ref. 1) are not sufficient to confirm consistency with a magma ocean model on Io., Comment: 8 pages, 2 figures, 2 tables

Quantum thermodynamics studies how quantum systems and operations may be exploited as sources of work to perform useful thermodynamic tasks. In real-world conditions, the evolution of open quantum systems typically displays memory effects, resulting in a non-Markovian dynamics. The associated information backflow has been observed to provide advantage in certain thermodynamic tasks. However, a general operational connection between non-Markovianity and thermodynamics in the quantum regime has remained elusive. Here, we analyze the role of non-Markovianity in the central task of extracting work via thermal operations from general multitime quantum processes, as described by process tensors. By defining a hierarchy of four classes of extraction protocols, expressed as quantum combs, we reveal three different physical mechanisms (work investment, multitime correlations, and system-environment correlations) through which non-Markovianity increases the work distillable from the process. The advantages arising from these mechanisms are linked precisely to a quantifier of the non-Markovianity of the process. These results show in very general terms how non-Markovianity of any given quantum process is a fundamental resource that unlocks an enhanced performance in thermodynamics.

We report recent observations of lava lakes within patera on Io made by the JIRAM imager/spectrometer on board the Juno spacecraft, taken during close observation occurred in the extended mission. At least 40 lava lakes have been identified from JIRAM observations. The majority (>50%) of paterae have elevated thermal signatures when imaged at sufficiently high spatial resolution (a few km/pixel), implying that lava lakes are ubiquitous on Io. The annular width of the spattering region around the margins, a characteristic of lava lakes, is of the order of few meters to tens of meters, the diameter of the observed lava lakes ranges from 10 to 100 km. The thickness of the crust in the center of some lava lakes is of the order of 5-10 m; we estimate that this crust is a few years old. Also, the bulk of the thermal emission comes from the much larger crust and not from the smaller exposed lava, so the total power output cannot be calculated from the 5-um radiance alone. Eight of the proposed lava lakes have never been reported previously as active hotspots.

We show how to entangle the motion of optically levitated nanoparticles in distant optical tweezers. The scheme consists in coupling the inelastically scattered light of each particle into transmission lines and directing it towards the other particle. The interference between this light and the background field introduces an effective coupling between the two particles while simultaneously reducing the effect of recoil heating. We analyze the system dynamics, showing that both transient and conditional entanglement between remote particles can be achieved under realistic experimental conditions.

Every massive particle behaves like a wave, according to quantum physics. Yet, this characteristic wave nature has only been observed in double-slit experiments with microscopic systems, such as atoms and molecules. The key aspect is that the wavefunction describing the motion of these systems extends coherently over a distance comparable to the slit separation, much larger than the size of the system itself. Preparing these states of more massive and complex objects remains an outstanding challenge. While the motion of solid-state oscillators can now be controlled at the level of single quanta, their coherence length remains comparable to the zero-point motion, limited to subatomic distances. Here, we prepare a delocalized state of a levitating solid-state nanosphere with coherence length exceeding the zero-point motion. We first cool its motion to the ground state. Then, by modulating the stiffness of the confinement potential, we achieve more than a threefold increment of the initial coherence length with minimal added noise. Optical levitation gives us the necessary control over the confinement that other mechanical platforms lack. Our work is a stepping stone towards the generation of delocalization scales comparable to the object size, a crucial regime for macroscopic quantum experiments, and towards quantum-enhanced force sensing with levitated particles.

Process tensors are quantum combs describing the evolution of open quantum systems through multiple steps of a quantum dynamics. While there is more than one way to measure how different two processes are, special care must be taken to ensure quantifiers obey physically desirable conditions such as data processing inequalities. Here, we analyze two classes of distinguishability measures commonly used in general applications of quantum combs. We show that the first class, called Choi divergences, does not satisfy an important data processing inequality, while the second one, which we call generalized divergences, does. We also extend to quantum combs some other relevant results of generalized divergences of quantum channels. Finally, given the properties we proved, we argue that generalized divergences may be more adequate than Choi divergences for distinguishing quantum combs in most of their applications. Particularly, this is crucial for defining monotones for resource theories whose states have a comb structure, such as resource theories of quantum processes and resource theories of quantum strategies.

Within a prediction task, Graph Neural Networks (GNNs) use relational information as an inductive bias to enhance the model's accuracy. As task-relevant relations might be unknown, graph structure learning approaches have been proposed to learn them while solving the downstream prediction task. In this paper, we demonstrate that minimization of a point-prediction loss function, e.g., the mean absolute error, does not guarantee proper learning of the latent relational information and its associated uncertainty. Conversely, we prove that a suitable loss function on the stochastic model outputs simultaneously grants (i) the unknown adjacency matrix latent distribution and (ii) optimal performance on the prediction task. Finally, we propose a sampling-based method that solves this joint learning task. Empirical results validate our theoretical claims and demonstrate the effectiveness of the proposed approach.

Modern graph representation learning works mostly under the assumption of dealing with regularly sampled temporal graph snapshots, which is far from realistic, e.g., social networks and physical systems are characterized by continuous dynamics and sporadic observations. To address this limitation, we introduce the Temporal Graph Ordinary Differential Equation (TG-ODE) framework, which learns both the temporal and spatial dynamics from graph streams where the intervals between observations are not regularly spaced. We empirically validate the proposed approach on several graph benchmarks, showing that TG-ODE can achieve state-of-the-art performance in irregular graph stream tasks., Comment: Preprint. Accepted at IJCAI 2024

Virtual sensing techniques allow for inferring signals at new unmonitored locations by exploiting spatio-temporal measurements coming from physical sensors at different locations. However, as the sensor coverage becomes sparse due to costs or other constraints, physical proximity cannot be used to support interpolation. In this paper, we overcome this challenge by leveraging dependencies between the target variable and a set of correlated variables (covariates) that can frequently be associated with each location of interest. From this viewpoint, covariates provide partial observability, and the problem consists of inferring values for unobserved channels by exploiting observations at other locations to learn how such variables can correlate. We introduce a novel graph-based methodology to exploit such relationships and design a graph deep learning architecture, named GgNet, implementing the framework. The proposed approach relies on propagating information over a nested graph structure that is used to learn dependencies between variables as well as locations. GgNet is extensively evaluated under different virtual sensing scenarios, demonstrating higher reconstruction accuracy compared to the state-of-the-art., Comment: Accepted at ICLR 2024

In the dynamics of open quantum systems, information may propagate in time through either the system or the environment, giving rise to Markovian and non-Markovian temporal correlations, respectively. However, despite their notable coexistence in most physical situations, it is not yet clear how these two quantities may limit the existence of one another. Here, we address this issue by deriving several inequalities relating the temporal correlations of general multi-time quantum processes. The dynamics are described by process tensors and the correlations are quantified by the mutual information between subsystems of their Choi states. First, we prove a set of upper bounds to the non-Markovianity of a process given the degree of Markovianity in each of its steps. This immediately implies a non-trivial maximum value for the non-Markovianity of any process, independently of its Markovianity. Finally, we obtain how the non-Markovianity limits the amount of total temporal correlations that could be present in a given process. These results show that, although any multi-time process must pay a price in total correlations to have a given amount of non-Markovianity, this price vanishes exponentially with the number of steps of the process, while the maximum non-Markovianity grows only linearly. This implies that even a highly non-Markovian process might be arbitrarily close to having maximum total correlations if it has a sufficiently large number of steps.

Proteins populate a manifold in the high-dimensional sequence space whose geometrical structure guides their natural evolution. Leveraging recently-developed structure prediction tools based on transformer models, we first examine the protein sequence landscape as defined by the folding score function. This landscape shares characteristics with optimization challenges encountered in machine learning and constraint satisfaction problems. Our analysis reveals that natural proteins predominantly reside in wide, flat minima within this energy landscape. To investigate further, we employ statistical mechanics algorithms specifically designed to explore regions with high local entropy in relatively flat landscapes. Our findings indicate that these specialized algorithms can identify valleys with higher entropy compared to those found using traditional methods such as Monte Carlo Markov Chains. In a proof-of-concept case, we find that these highly entropic minima exhibit significant similarities to natural sequences, especially in critical key sites and local entropy. Additionally, evaluations through Molecular Dynamics suggests that the stability of these sequences closely resembles that of natural proteins. Our tool combines advancements in machine learning and statistical physics, providing new insights into the exploration of sequence landscapes where wide, flat minima coexist alongside a majority of narrower minima.

Graph-based deep learning methods have become popular tools to process collections of correlated time series. Differently from traditional multivariate forecasting methods, neural graph-based predictors take advantage of pairwise relationships by conditioning forecasts on a (possibly dynamic) graph spanning the time series collection. The conditioning can take the form of an architectural inductive bias on the neural forecasting architecture, resulting in a family of deep learning models called spatiotemporal graph neural networks. Such relational inductive biases enable the training of global forecasting models on large time-series collections, while at the same time localizing predictions w.r.t. each element in the set (i.e., graph nodes) by accounting for local correlations among them (i.e., graph edges). Indeed, recent theoretical and practical advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing frameworks appealing and timely. However, most of the studies in the literature focus on proposing variations of existing neural architectures by taking advantage of modern deep learning practices, while foundational and methodological aspects have not been subject to systematic investigation. To fill the gap, this paper aims to introduce a comprehensive methodological framework that formalizes the forecasting problem and provides design principles for graph-based predictive models and methods to assess their performance. At the same time, together with an overview of the field, we provide design guidelines, recommendations, and best practices, as well as an in-depth discussion of open challenges and future research directions.

Juno has allowed clear, high-resolution imaging of Io's polar volcanoes using the Jovian Infrared Auroral Mapper (JIRAM) instrument. We have used data from JIRAM's M-band (4.78 um) imager from eleven Juno orbits to construct a global map of volcanic flux. This map provides short-term insight into the spatial distribution of volcanoes and the ways in which high- and low-latitude volcanoes differ. Using spherical harmonic analysis, we quantitatively compare our volcanic flux map to the surface heat flow distribution expected from models of Io's tidal heat deposition (summarized in de Kleer et al. 2019). Our observations confirm previously detected systems of bright volcanoes at high latitudes. Our study finds that both poles are comparably active and that the observed flux distribution is inconsistent with an asthenospheric heating model, although the south pole is viewed too infrequently to establish reliable trends., Comment: 11 pages, 3 figures

Time series are the primary data type used to record dynamic system measurements and generated in great volume by both physical sensors and online processes (virtual sensors). Time series analytics is therefore crucial to unlocking the wealth of information implicit in available data. With the recent advancements in graph neural networks (GNNs), there has been a surge in GNN-based approaches for time series analysis. These approaches can explicitly model inter-temporal and inter-variable relationships, which traditional and other deep neural network-based methods struggle to do. In this survey, we provide a comprehensive review of graph neural networks for time series analysis (GNN4TS), encompassing four fundamental dimensions: forecasting, classification, anomaly detection, and imputation. Our aim is to guide designers and practitioners to understand, build applications, and advance research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy of GNN4TS. Then, we present and discuss representative research works and introduce mainstream applications of GNN4TS. A comprehensive discussion of potential future research directions completes the survey. This survey, for the first time, brings together a vast array of knowledge on GNN-based time series research, highlighting foundations, practical applications, and opportunities of graph neural networks for time series analysis., Comment: 37 pages, 6 figures, 7 tables; Project page: https://github.com/KimMeen/Awesome-GNN4TS

The purpose of this paper is to extend the store of models able to support integrable defects by investigating the two-dimensional Boussinesq nonlinear wave equation. As has been previously noted in many examples, insisting that a defect contributes to energy and momentum to ensure their conservation, despite the presence of discontinuities and the explicit breaking of translation invariance, leads to sewing conditions relating the two fields and their derivatives on either side of the defect. The manner in which several types of soliton solutions to the Boussinesq equation are affected by the defect is explored and reveals new effects that have not been observed in other integrable systems, such as the possibility of a soliton reflecting from a defect or of a defect decaying into one or two solitons., Comment: 28 pages, 9 figures

We present general reduction procedures for Courant, Dirac and generalized complex structures, in particular when a group of symmetries is acting. We do so by taking the graded symplectic viewpoint on Courant algebroids and carrying out graded symplectic reduction, both in the coisotropic and hamiltonian settings. Specializing the latter to the exact case, we recover in a systematic way the reduction schemes of Bursztyn-Cavalcanti-Gualtieri., Comment: 80 pages. v2: Added Lemma 7.1. Added Example 6.15 and consequences thereof (Examples 7.6, 7.7, 7.12, 8.20, 8.21, 8.22)

In the companion paper arXiv:2110.05298, we developed the deformation theory of symplectic foliations, focusing on geometric aspects. Here, we address some algebraic questions that arose naturally. We show that the $L_{\infty}$-algebra constructed there is independent of the choices made, and we prove that the gauge equivalence of Maurer-Cartan elements corresponds to the equivalence by isotopies of symplectic foliations., Comment: 26 pages

Given an $L_{\infty}$-algebra $V$ and an $L_{\infty}$-subalgebra $W$, we give sufficient conditions for all small Maurer-Cartan elements of $V$ to be equivalent to Maurer-Cartan elements lying in $W$. As an application, we obtain a stability criterion for fixed points of a Dirac structure (for instance a twisted Poisson structure), i.e. points where the corresponding leaf is zero-dimensional. The criterion guarantees that any nearby Dirac structure also has a fixed point., Comment: Final version, accepted for publication. 22 pages

Developing protocols for preserving information in quantum systems is a central quest for implementing realistic quantum computation. In this regard, the quantum Zeno effect has emerged as a widely utilized technique to safeguard classical information stored in quantum systems. However, existing results pertaining to this method often assume operations performed infinitely fast on the system of interest, which only serves as an approximation to real-world scenarios where the temporal resolution of any experimental apparatus is inherently finite. In this study, we go beyond this conventional assumption and derive the effective Zeno dynamics for any time interval between operations. Our analysis considers a qubit undergoing thermalization, as described by a generalized amplitude damping channel, while the operations performed consist of projections onto an orthonormal basis that may or may not coincide with the pointer basis to which the system is thermalizing. By obtaining the probability of successfully storing a bit of information after a given time, we investigate the performance of the protocol in two important scenarios: the limit of many interventions, with a first-order correction to the Zeno limit, and the limit of very few interventions. In doing so, we provide valuable insights into the protocol's performance by establishing bounds on its efficacy. These findings enhance our understanding of the practical applicability of the quantum Zeno effect in preserving classical information stored in quantum systems, allowing for better design and optimization of quantum information processing protocols.

Reconciliation enforces coherence between hierarchical forecasts, in order to satisfy a set of linear constraints. While most works focus on the reconciliation of the point forecasts, we consider probabilistic reconciliation and we analyze the properties of the distributions reconciled via conditioning. We provide a formal analysis of the variance of the reconciled distribution, treating separately the case of Gaussian forecasts and count forecasts. We also study the reconciled upper mean in the case of 1-level hierarchies; also in this case we analyze separately the case of Gaussian forecasts and count forecasts. We then show experiments on the reconciliation of intermittent time series related to the count of extreme market events. The experiments confirm our theoretical results and show that reconciliation largely improves the performance of probabilistic forecasting., Comment: 23 pages, 6 figures

The well-known Kalman filters model dynamical systems by relying on state-space representations with the next state updated, and its uncertainty controlled, by fresh information associated with newly observed system outputs. This paper generalizes, for the first time in the literature, Kalman and extended Kalman filters to discrete-time settings where inputs, states, and outputs are represented as attributed graphs whose topology and attributes can change with time. The setup allows us to adapt the framework to cases where the output is a vector or a scalar too (node/graph level tasks). Within the proposed theoretical framework, the unknown state-transition and the readout functions are learned end-to-end along with the downstream prediction task., Comment: Added empirical validation

Spatiotemporal graph neural networks have shown to be effective in time series forecasting applications, achieving better performance than standard univariate predictors in several settings. These architectures take advantage of a graph structure and relational inductive biases to learn a single (global) inductive model to predict any number of the input time series, each associated with a graph node. Despite the gain achieved in computational and data efficiency w.r.t. fitting a set of local models, relying on a single global model can be a limitation whenever some of the time series are generated by a different spatiotemporal stochastic process. The main objective of this paper is to understand the interplay between globality and locality in graph-based spatiotemporal forecasting, while contextually proposing a methodological framework to rationalize the practice of including trainable node embeddings in such architectures. We ascribe to trainable node embeddings the role of amortizing the learning of specialized components. Moreover, embeddings allow for 1) effectively combining the advantages of shared message-passing layers with node-specific parameters and 2) efficiently transferring the learned model to new node sets. Supported by strong empirical evidence, we provide insights and guidelines for specializing graph-based models to the dynamics of each time series and show how this aspect plays a crucial role in obtaining accurate predictions., Comment: Accepted at NeurIPS 2023

This paper introduces a novel residual correlation analysis, called AZ-analysis, to assess the optimality of spatio-temporal predictive models. The proposed AZ-analysis constitutes a valuable asset for discovering and highlighting those space-time regions where the model can be improved with respect to performance. The AZ-analysis operates under very mild assumptions and is based on a spatio-temporal graph that encodes serial and functional dependencies in the data; asymptotically distribution-free summary statistics identify existing residual correlation in space and time regions, hence localizing time frames and/or communities of sensors, where the predictor can be improved.

State-space models constitute an effective modeling tool to describe multivariate time series and operate by maintaining an updated representation of the system state from which predictions are made. Within this framework, relational inductive biases, e.g., associated with functional dependencies existing among signals, are not explicitly exploited leaving unattended great opportunities for effective modeling approaches. The manuscript aims, for the first time, at filling this gap by matching state-space modeling and spatio-temporal data where the relational information, say the functional graph capturing latent dependencies, is learned directly from data and is allowed to change over time. Within a probabilistic formulation that accounts for the uncertainty in the data-generating process, an encoder-decoder architecture is proposed to learn the state-space model end-to-end on a downstream task. The proposed methodological framework generalizes several state-of-the-art methods and demonstrates to be effective in extracting meaningful relational information while achieving optimal forecasting performance in controlled environments.

Hierarchical time series are common in several applied fields. The forecasts for these time series are required to be coherent, that is, to satisfy the constraints given by the hierarchy. The most popular technique to enforce coherence is called reconciliation, which adjusts the base forecasts computed for each time series. However, recent works on probabilistic reconciliation present several limitations. In this paper, we propose a new approach based on conditioning to reconcile any type of forecast distribution. We then introduce a new algorithm, called Bottom-Up Importance Sampling, to efficiently sample from the reconciled distribution. It can be used for any base forecast distribution: discrete, continuous, or in the form of samples, providing a major speedup compared to the current methods. Experiments on several temporal hierarchies show a significant improvement over base probabilistic forecasts., Comment: 27 pages, 4 figures