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The inference of causal relationships among observed variables is a pivotal, longstanding problem in the scientific community. An intuitive method for quantifying these causal links involves examining the response of one variable to perturbations in another. The fluctuation-dissipation theorem elegantly connects this response to the correlation functions of the unperturbed system, thereby bridging the concepts of causality and correlation. However, this relationship becomes intricate in nonlinear systems, where knowledge of the invariant measure is required but elusive, especially in high-dimensional spaces. In this study, we establish a novel link between the Koopman operator of nonlinear stochastic systems and the response function. This connection provides an alternative method for computing the response function using generalized correlation functions, even when the invariant measure is unknown. We validate our theoretical framework by applying it to a nonlinear high-dimensional system amenable to exact solutions, demonstrating convergence and consistency with established results. Finally, we discuss a significant interplay between the resulting causal network and the relevant time scales of the system.

In their comment (1), Hawreliak et al. claims that our observation of stacking fault formation and transonic dislocation propagation in diamond (2) is not valid as they interpret the observed features as cracks. In this response letter, we describe our rationale for interpreting the observed features as stacking faults. We also address other points raised in their comments, including the clarifications of how the results of Makarov et al. (3) are not in conflict with our study., Comment: Comment on arXiv:2401.04213. 10 pages, 2 figures

We present measurements on Fe$_2$O$_3$ amorphization and melt under laser-driven shock compression up to 209(10) GPa via time-resolved in situ x-ray diffraction. At 122(3) GPa, a diffuse signal is observed indicating the presence of a non-crystalline phase. Structure factors have been extracted up to 182(6) GPa showing the presence of two well-defined peaks. A rapid change in the intensity ratio of the two peaks is identified between 145(10) and 151(10) GPa, indicative of a phase change. Present DFT+$U$ calculations of temperatures along Fe$_2$O$_3$ Hugoniot are in agreement with SESAME 7440 and indicate relatively low temperatures, below 2000 K, up to 150 GPa. The non-crystalline diffuse scattering is thus consistent with the - as yet unreported - shock amorphization of Fe$_2$O$_3$ between 122(3) and 145(10) GPa, followed by an amorphous-to-liquid transition above 151(10) GPa. Upon release, a non-crystalline phase is observed alongside crystalline $\alpha$-Fe$_2$O$_3$. The extracted structure factor and pair distribution function of this release phase resemble those reported for Fe$_2$O$_3$ melt at ambient pressure., Comment: 11 pages, 4 figures, under review

Congestion games are attractive because they can model many concrete situations where some competing entities interact through the use of some shared resources, and also because they always admit pure Nash equilibria which correspond to the local minima of a potential function. We explore the problem of computing a state of minimum potential in this setting. Using the maximum number of resources that a player can use at a time, and the possible symmetry in the players' strategy spaces, we settle the complexity of the problem for instances having monotone (i.e., either non-decreasing or non-increasing) latency functions on their resources. The picture, delineating polynomial and NP-hard cases, is complemented with tight approximation algorithms.

We report here the first equation of state measurements of Fe$_2$O$_3$ obtained with laser-driven shock compression. The data are in excellent agreement with previous dynamic and static compression measurements at low pressure, and extend the known Hugoniot up to 700 GPa. We observe a large volume drop of $\sim$10% at 86 GPa, which could be associated, according to static compression observations, with the iron spin transition. Our measurements also suggest a change of the Hugoniot curve between 150 and 250 GPa. Above 250 GPa and within our error bars, we do not observe significant modifications up to the maximum pressure of 700 GPa reached in our experiment., Comment: 8 pages, 3 figures, 2 tables

In this work, we study the Stochastic Budgeted Multi-round Submodular Maximization (SBMSm) problem, where we aim to adaptively maximize the sum, over multiple rounds, of a monotone and submodular objective function defined on subsets of items. The objective function also depends on the realization of stochastic events, and the total number of items we can select over all rounds is bounded by a limited budget. This problem extends, and generalizes to multiple round settings, well-studied problems such as (adaptive) influence maximization and stochastic probing. We show that, if the number of items and stochastic events is somehow bounded, there is a polynomial time dynamic programming algorithm for SBMSm. Then, we provide a simple greedy $1/2(1-1/e-\epsilon)\approx 0.316$-approximation algorithm for SBMSm, that first non-adaptively allocates the budget to be spent at each round, and then greedily and adaptively maximizes the objective function by using the budget assigned at each round. Finally, we introduce the {\em budget-adaptivity gap}, by which we measure how much an adaptive policy for SBMSm is better than an optimal partially adaptive one that, as in our greedy algorithm, determines the budget allocation in advance. We show that the budget-adaptivity gap lies between $e/(e-1)\approx 1.582$ and $2$.

Local networks of neurons are nonlinear systems driven by synaptic currents elicited by its own spiking activity and the input received from other brain areas. Synaptic currents are well approximated by correlated Gaussian noise. Besides, the population dynamics of neuronal networks is often found to be multistable, allowing the noise source to induce state transitions. State changes in neuronal systems underlies the way information is encoded and transformed. The characterization of the escape time from metastable states is then a cornerstone to understand how information is processed in the brain. The effects of correlated input forcing bistable systems have been studied for over half a century, nonetheless most results are perturbative or valid only when a separation of time scales is present. Here, we present a novel and exact result holding when the correlation time of the noise source is identical to that of the neural population, hence solving in a very general setting the mean escape time problem.

Covariance matrix estimation is an important task in the analysis of multivariate data in disparate scientific fields, including neuroscience, genomics, and astronomy. However, modern scientific data are often incomplete due to factors beyond the control of researchers, and data missingness may prohibit the use of traditional covariance estimation methods. Some existing methods address this problem by completing the data matrix, or by filling the missing entries of an incomplete sample covariance matrix by assuming a low-rank structure. We propose a novel approach that exploits auxiliary variables to complete covariance matrix estimates. An example of auxiliary variable is the distance between neurons, which is usually inversely related to the strength of neuronal correlation. Our method extracts auxiliary information via regression, and involves a single tuning parameter that can be selected empirically. We compare our method with other matrix completion approaches via simulations, and apply it to the analysis of large-scale neuroscience data., Comment: 16 pages, 6 figures

Researchers continue exploring neurons' intricate patterns of activity in the cerebral visual cortex in response to visual stimuli. The way neurons communicate and optimize their interactions with each other under different experimental conditions remains a topic of active investigation. Probabilistic Graphical Models are invaluable tools in neuroscience research, as they let us identify the functional connections, or conditional statistical dependencies, between neurons. Graphical models represent these connections as a graph, where nodes represent neurons and edges indicate the presence of functional connections between them. We developed the R package neurofuncon for the computation and visualization of functional connectivity graphs from large-scale data based on the Graphical lasso. We illustrate the use of this package with publicly available two-photon calcium microscopy imaging data from approximately 10000 neurons in a 1mm cubic section of a mouse visual cortex., Comment: 7 pages, 5 figures

Modern Cloud/Edge architectures need to orchestrate multiple layers of heterogeneous computing nodes, including pervasive sensors/actuators, distributed Edge/Fog nodes, centralized data centers and quantum devices. The optimal assignment and scheduling of computation on the different nodes is a very difficult problem, with NP-hard complexity. In this paper, we explore the possibility of solving this problem with Variational Quantum Algorithms, which can become a viable alternative to classical algorithms in the near future. In particular, we compare the performances, in terms of success probability, of two algorithms, i.e., Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE). The simulation experiments, performed for a set of simple problems, %CM230124 that involve a Cloud and two Edge nodes, show that the VQE algorithm ensures better performances when it is equipped with appropriate circuit \textit{ansatzes} that are able to restrict the search space. Moreover, experiments executed on real quantum hardware show that the execution time, when increasing the size of the problem, grows much more slowly than the trend obtained with classical computation, which is known to be exponential., Comment: 14 pages, 13 figures

Factor models are widely used in the analysis of high-dimensional data in several fields of research. Estimating a factor model, in particular its covariance matrix, from partially observed data vectors is very challenging. In this work, we show that when the data are structurally incomplete, the factor model likelihood function can be decomposed into the product of the likelihood functions of multiple partial factor models relative to different subsets of data. If these multiple partial factor models are linked together by common parameters, then we can obtain complete maximum likelihood estimates of the factor model parameters and thereby the full covariance matrix. We call this framework Linked Factor Analysis (LINFA). LINFA can be used for covariance matrix completion, dimension reduction, data completion, and graphical dependence structure recovery. We propose an efficient Expectation-Maximization algorithm for maximum likelihood estimation, accelerated by a novel group vertex tessellation (GVT) algorithm which identifies a minimal partition of the vertex set to implement an efficient optimization in the maximization steps. We illustrate our approach in an extensive simulation study and in the analysis of calcium imaging data collected from mouse visual cortex., Comment: 21 page, 9 figures

The persistent issue of wrongful convictions in the United States emphasizes the need for scrutiny and improvement of the criminal justice system. While statistical methods for the evaluation of forensic evidence, including glass, fingerprints, and DNA, have significantly contributed to solving intricate crimes, there is a notable lack of national-level standards to ensure the appropriate application of statistics in forensic investigations. We discuss the obstacles in the application of statistics in court, and emphasize the importance of making statistical interpretation accessible to non-statisticians, especially those who make decisions about potentially innocent individuals. We investigate the use and misuse of statistical methods in crime investigations, in particular the likelihood ratio approach. We further describe the use of graphical models, where hypotheses and evidence can be represented as nodes connected by arrows signifying association or causality. We emphasize the advantages of special graph structures, such as object-oriented Bayesian networks and chain event graphs, which allow for the concurrent examination of evidence of various nature., Comment: 20 pages, 8 figures

The efficient management of energy communities relies on the solution of the "prosumer problem", i.e., the problem of scheduling the household loads on the basis of the user needs, the electricity prices, and the availability of local renewable energy, with the aim of reducing costs and energy waste. Quantum computers can offer a significant breakthrough in treating this problem thanks to the intrinsic parallel nature of quantum operations. The most promising approach is to devise variational hybrid algorithms, in which quantum computation is driven by parameters that are optimized classically, in a cycle that aims at finding the best solution with a significant speed-up with respect to classical approaches. This paper provides a reformulation of the prosumer problem, allowing to address it with a hybrid quantum algorithm, namely, Quantum Approximate Optimization Algorithm (QAOA), and with a recent variant, the Recursive QAOA. We report on an extensive set of experiments, on simulators and real quantum hardware, for different problem sizes. Results are encouraging in that Recursive QAOA is able, for problems involving up to 10 qubits, to provide optimal and admissible solutions with good probabilities, while the computation time is nearly independent of the system size, Comment: 14 pages, 13 figures. IEEE Transactions on Smart Grid (2023)

Data standardization has become one of the leading methods neuroimaging researchers rely on for data sharing and reproducibility. Data standardization promotes a common framework through which researchers can utilize others' data. Yet, as of today, formatting datasets that adhere to community best practices requires technical expertise involving coding and considerable knowledge of file formats and standards. We describe ezBIDS, a tool for converting neuroimaging data and associated metadata to the Brain Imaging Data Structure (BIDS) standard. ezBIDS provides four unique features: (1) No installation or programming requirements. (2) Handling of both imaging and task events data and metadata. (3) Automated inference and guidance for adherence to BIDS. (4) Multiple data management options: download BIDS data to local system, or transfer to OpenNeuro.org or brainlife.io. In sum, ezBIDS requires neither coding proficiency nor knowledge of BIDS and is the first BIDS tool to offer guided standardization, support for task events conversion, and interoperability with OpenNeuro and brainlife.io.

The classification of galaxy morphologies is an important step in the investigation of theories of hierarchical structure formation. While human expert visual classification remains quite effective and accurate, it cannot keep up with the massive influx of data from emerging sky surveys. A variety of approaches have been proposed to classify large numbers of galaxies; these approaches include crowdsourced visual classification, and automated and computational methods, such as machine learning methods based on designed morphology statistics and deep learning. In this work, we develop two novel galaxy morphology statistics, descent average and descent variance, which can be efficiently extracted from telescope galaxy images. We further propose simplified versions of the existing image statistics concentration, asymmetry, and clumpiness, which have been widely used in the literature of galaxy morphologies. We utilize the galaxy image data from the Sloan Digital Sky Survey to demonstrate the effective performance of our proposed image statistics at accurately detecting spiral and elliptical galaxies when used as features of a random forest classifier., Comment: 11 pages, 6 figures

Neuroscience research has expanded dramatically over the past 30 years by advancing standardization and tool development to support rigor and transparency. Consequently, the complexity of the data pipeline has also increased, hindering access to FAIR (Findable, Accessible, Interoperabile, and Reusable) data analysis to portions of the worldwide research community. brainlife.io was developed to reduce these burdens and democratize modern neuroscience research across institutions and career levels. Using community software and hardware infrastructure, the platform provides open-source data standardization, management, visualization, and processing and simplifies the data pipeline. brainlife.io automatically tracks the provenance history of thousands of data objects, supporting simplicity, efficiency, and transparency in neuroscience research. Here brainlife.io's technology and data services are described and evaluated for validity, reliability, reproducibility, replicability, and scientific utility. Using data from 4 modalities and 3,200 participants, we demonstrate that brainlife.io's services produce outputs that adhere to best practices in modern neuroscience research.

Taking informed decisions, namely acting rationally, is an individual attitude of paramount relevance in nature and human societies. In this work, we study how rationality spreads in a community. To this end, through an agent-based model, we analyse the dynamics of a population whose individuals, endowed with a rational attitude controlled by a numerical parameter, play a simple game. The latter consists of multiple strategies, each associated with a given reward. The proposed model is then used as a benchmark for studying the behaviour of Bitcoin users, inferred by analysing transactions recorded in the Blockchain. Remarkably, a population undergoing a sharp transition from irrational to rational attitudes shows a behavioural pattern similar to that of Bitcoin users, whose rationality showed up as soon as their cryptocurrency became worth just a few cents (USD). To conclude, a behavioural analysis that relies on an entropy measure combined with a simple agent-based model allows us to detect the rise of rationality across a community. Although further investigations are essential to corroborate our results, we deem the proposed approach could also get used for studying other social phenomena and behaviours., Comment: 10 pages, 5 figures

Deep generative learning cannot only be used for generating new data with statistical characteristics derived from input data but also for anomaly detection, by separating nominal and anomalous instances based on their reconstruction quality. In this paper, we explore the performance of three unsupervised deep generative models -- variational autoencoders (VAEs) with Gaussian, Bernoulli, and Boltzmann priors -- in detecting anomalies in flight-operations data of commercial flights consisting of multivariate time series. We devised two VAE models with discrete latent variables (DVAEs), one with a factorized Bernoulli prior and one with a restricted Boltzmann machine (RBM) as prior, because of the demand for discrete-variable models in machine-learning applications and because the integration of quantum devices based on two-level quantum systems requires such models. The DVAE with RBM prior, using a relatively simple -- and classically or quantum-mechanically enhanceable -- sampling technique for the evolution of the RBM's negative phase, performed better than the Bernoulli DVAE and on par with the Gaussian model, which has a continuous latent space. Our studies demonstrate the competitiveness of a discrete deep generative model with its Gaussian counterpart on anomaly-detection tasks. Moreover, the DVAE model with RBM prior can be easily integrated with quantum sampling by outsourcing its generative process to measurements of quantum states obtained from a quantum annealer or gate-model device., Comment: 25 pages, 7 figures, 3 tables, appendix, supplementary material

The motion of line defects (dislocations) has been studied for over 60 years but the maximum speed at which they can move is unresolved. Recent models and atomistic simulations predict the existence of a limiting velocity of dislocation motions between the transonic and subsonic ranges at which the self-energy of dislocation diverges, though they do not deny the possibility of the transonic dislocations. We use femtosecond x-ray radiography to track ultrafast dislocation motion in shock-compressed single-crystal diamond. By visualizing stacking faults extending faster than the slowest sound wave speed of diamond, we show the evidence of partial dislocations at their leading edge moving transonically. Understanding the upper limit of dislocation mobility in crystals is essential to accurately model, predict, and control the mechanical properties of materials under extreme conditions.