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Accurate prediction of electricity day-ahead prices is essential in competitive electricity markets. Although stationary electricity-price forecasting techniques have received considerable attention, research on non-stationary methods is comparatively scarce, despite the common prevalence of non-stationary features in electricity markets. Specifically, existing non-stationary techniques will often aim to address individual non-stationary features in isolation, leaving aside the exploration of concurrent multiple non-stationary effects. Our overarching objective here is the formulation of a framework to systematically model and forecast non-stationary electricity-price time series, encompassing the broader scope of non-stationary behavior. For this purpose we develop a data-driven model that combines an N-dimensional Langevin equation (LE) with a neural-ordinary differential equation (NODE). The LE captures fine-grained details of the electricity-price behavior in stationary regimes but is inadequate for non-stationary conditions. To overcome this inherent limitation, we adopt a NODE approach to learn, and at the same time predict, the difference between the actual electricity-price time series and the simulated price trajectories generated by the LE. By learning this difference, the NODE reconstructs the non-stationary components of the time series that the LE is not able to capture. We exemplify the effectiveness of our framework using the Spanish electricity day-ahead market as a prototypical case study. Our findings reveal that the NODE nicely complements the LE, providing a comprehensive strategy to tackle both stationary and non-stationary electricity-price behavior. The framework's dependability and robustness is demonstrated through different non-stationary scenarios by comparing it against a range of basic naive methods., Comment: 26 pages, 7 figures

The swift progression of machine learning (ML) has not gone unnoticed in the realm of statistical mechanics. ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable discovery of free-energy functionals to determine the equilibrium-density profile of a many-particle system. Within DFT, the external potential accounts for the interaction of the many-particle system with an external field, thus, affecting the density distribution. In this context, we introduce a statistical-learning framework to infer the external potential exerted on a many-particle system. We combine a Bayesian inference approach with the classical DFT apparatus to reconstruct the external potential, yielding a probabilistic description of the external potential functional form with inherent uncertainty quantification. Our framework is exemplified with a grand-canonical one-dimensional particle ensemble with excluded volume interactions in a confined geometry. The required training dataset is generated using a Monte Carlo (MC) simulation where the external potential is applied to the grand-canonical ensemble. The resulting particle coordinates from the MC simulation are fed into the learning framework to uncover the external potential. This eventually allows us to compute the equilibrium density profile of the system by using the tools of DFT. Our approach benchmarks the inferred density against the exact one calculated through the DFT formulation with the true external potential. The proposed Bayesian procedure accurately infers the external potential and the density profile. We also highlight the external-potential uncertainty quantification conditioned on the amount of available simulated data. The seemingly simple case study introduced in this work might serve as a prototype for studying a wide variety of applications, including adsorption and capillarity.

Remote patient monitoring (RPM) technologies have been identified as a viable alternative to improve access to care in underserved communities. Successful RPM platforms are designed and implemented for seamless integration into healthcare providers work to increase adoption and availability for offering remote care. A quantitative survey was designed and administered to elicit perspectives from a wide range of stakeholders, including healthcare providers and healthcare administrators, about barriers and facilitators in the adoption and integration of RPM into clinical workflows in underserved areas. Ease of adoption, workflow disruption, changes in the patient-physician relationship, and costs and financial benefits are identified as relevant factors that influence the widespread use of RPM by healthcare providers; significant communication and other implementation preferences also emerged. Further research is needed to identify methods to address such concerns and use information collected in this study to develop protocols for RPM integration into clinical workflow.

We study for the first time the low-frequency ($\sim$150 MHz) radio brightness distribution of Arp~299 at subarcsecond resolution, tracing in both compact and extended emission regions the local spectral energy distribution (SED) in order to characterize the dominant emission and absorption processes. We analysed the spatially resolved emission of Arp 299 revealed by 150 MHz international baseline Low-Frequency Array (LOFAR) and 1.4, 5.0, and 8.4 GHz Very Large Array (VLA) observations. We present the first subarcsecond (0.4"$\sim$100~pc) image of the whole Arp~299 system at 150~MHz. The high surface brightness sensitivity of our LOFAR observations ($\sim$100 $\mu$Jy/beam) allowed us to detect all of the nuclear components detected at higher frequencies, as well as the extended steep-spectrum emission surrounding the nuclei. We obtained spatially resolved, two-point spectral index maps for the whole galaxy: the compact nuclei show relatively flat spectra, while the extended, diffuse component shows a steep spectrum. We fitted the radio SED of the nuclear regions using two different models: a continuous free-free medium model and a clumpy model. The continuous model can explain the SED of the nuclei assuming a population of relativistic electrons subjected to synchrotron, bremsstrahlung, and ionization losses. The clumpy model fits assuming relativistic electrons with negligible energy losses, and thermal fractions that are more typical of star-forming galaxies than those required for the continuous model. Our results confirm the usefulness of combining spatially resolved radio imaging at both MHz and GHz frequencies to characterize in detail the radio emission properties of LIRGs from the central 100 pc out to the kiloparsec galaxy-wide scales., Comment: Accepted / Submitted to a special issue of A&A on sub-arcsecond imaging with LOFAR

We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed scheme deals with general free-energy functionals, including, for instance, external fields or interaction potentials. This allows us to simulate a range of physical phenomena where thermal fluctuations play a crucial role, such as nucleation and other energy-barrier crossing transitions. A positivity-preserving algorithm for the density is derived based on a hybrid space discretization of the deterministic and the stochastic terms and different implicit and explicit time integrators. We show through numerous applications that not only our scheme is able to accurately reproduce the statistical properties (structure factor and correlations) of the physical system, but, because of the multiplicative noise, it allows us to simulate energy barrier crossing dynamics, which cannot be captured by mean-field approaches.

Finding the dynamical law of observable quantities lies at the core of physics. Within the particular field of statistical mechanics, the generalized Langevin equation (GLE) comprises a general model for the evolution of observables covering a great deal of physical systems with many degrees of freedom and an inherently stochastic nature. Although formally exact, the GLE brings its own great challenges. It depends on the complete history of the observables under scrutiny, as well as the microscopic degrees of freedom, all of which are often inaccessible. We show that these drawbacks can be overcome by adopting elements of machine learning from empirical data, in particular coupling a multilayer perceptron (MLP) with the formal structure of the GLE and calibrating the MLP with the data. This yields a powerful computational tool capable of describing noisy complex systems beyond the realms of statistical mechanics. It is exemplified with a number of representative examples from different fields: from a single colloidal particle and particle chains in a thermal bath to climatology and finance, showing in all cases excellent agreement with the actual observable dynamics. The new framework offers an alternative perspective for the study of non-equilibrium processes opening also a new route for stochastic modelling.

Tidal disruption events (TDEs) are transient flares produced when a star is ripped apart by the gravitational field of a supermassive black hole (SMBH). We have observed a transient source in the western nucleus of the merging galaxy pair Arp 299 that radiated >1.5x10^52 erg in the infrared and radio, but was not luminous at optical or X-ray wavelengths. We interpret this as a TDE with much of its emission re-radiated at infrared wavelengths by dust. Efficient reprocessing by dense gas and dust may explain the difference between theoretical predictions and observed luminosities of TDEs. The radio observations resolve an expanding and decelerating jet, probing the jet formation and evolution around a SMBH., Comment: Published online by Science on 14 Jun 2018

We report on the first sub-arcsecond (0.44 $\times$ 0.41 arcsec$\rm ^2$) angular resolution image at 150 MHz of the A-nucleus in the Luminous Infrared Galaxy Arp$\,$299, from International Low Frequency Array (LOFAR) Telescope observations. The most remarkable finding is that of an intriguing two-sided, filamentary structure emanating from A-nucleus, which we interpret as an outflow that extends up to at least 14 arcseconds from the A-nucleus in the N-S direction ($\approx$ 5 kpc deprojected size) and accounts for almost 40% of the extended emission of the entire galaxy system. We also discuss HST/NICMOS [FeII] 1.64 $\rm \mu m$ and H$\rm_2$ 2.12 $\rm \mu m$ images of Arp$\,$299-A, which show similar features to those unveiled by our 150 MHz LOFAR observations, thus giving string morphological support for the outflow scenario. Finally, we discuss unpublished NaI D spectra that confirm the outflow nature of this structure. From energetic arguments, we rule out the low-luminosity active galactic nucleus in Arp$\,$299-A as a driver for the outflow. On the contrary, the powerful, compact starburst in the central regions of Arp$\,$299-A provides plenty of mechanical energy to sustain an outflow, and we conclude that the intense supernova (SN) activity in the nuclear region of Arp299-A is driving the observed outflow. We estimate that the starburst wind can support a mass-outflow rate in the range (11-63) $\rm M_{\odot} yr^{-1}$ at speeds of up to (370 - 890) $\rm km \, s^{-1}$, and is relatively young, with an estimated kinematic age of (3 - 7) Myr. Those results open an avenue to the use of low-frequency (150 MHz), sub-arcsecond imaging with LOFAR to detect outflows in the central regions of local luminous infrared galaxies.

Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be understood. An example of this is dewetting, which involves the rupture of a thin liquid film and the formation of droplets. Such a process is thermally activated and requires fluctuations to be taken into account self-consistently. In this work we present an analytical and numerical study of a stochastic thin-film equation derived from first principles. Following a brief review of the derivation, we scrutinise the behaviour of the equation in the limit of perfectly correlated noise along the wall-normal direction. The stochastic thin-film equation is also simulated by adopting a numerical scheme based on a spectral collocation method. The scheme allows us to explore the fluctuating dynamics of the thin film and the behaviour of its free energy in the vicinity of rupture. Finally, we also study the effect of the noise intensity on the rupture time, which is in agreement with previous works., Comment: 23 pages, 8 figures, Published version J Stat Phys (2019)

We present the final data release of the APEX low-redshift legacy survey for molecular gas (ALLSMOG), comprising CO(2-1) emission line observations of 88 nearby, low-mass (10^8.5

We analyse new observations with the International Low Frequency Array (LOFAR) telescope, and archival data from the Multi-Element Radio Linked Interferometer Network (MERLIN) and the Karl G. Jansky Very Large Array (VLA). We model the spatially resolved radio spectrum of Arp 220 from 150 MHz to 33 GHz. We present an image of Arp 220 at 150 MHz with resolution $0.65''\times0.35''$, sensitivity 0.15 mJy beam$^{-1}$, and integrated flux density $394\pm59$ mJy. More than 80% of the detected flux comes from extended ($6''\approx$2.2 kpc) steep spectrum ($\alpha=-0.7$) emission, likely from star formation in the molecular disk surrounding the two nuclei. We find elongated features extending $0.3''$ (110 pc) and $0.9''$ (330 pc) from the eastern and western nucleus respectively, which we interpret as evidence for outflows. The extent of radio emission requires acceleration of cosmic rays far outside the nuclei. We find that a simple three component model can explain most of the observed radio spectrum of the galaxy. When accounting for absorption at 1.4 GHz, Arp 220 follows the FIR/radio correlation with $q=2.36$, and we estimate a star formation rate of 220 M$_\odot\text{yr}^{-1}$. We derive thermal fractions at 1 GHz of less than 1% for the nuclei, which indicates that a major part of the UV-photons are absorbed by dust. International LOFAR observations shows great promise to detect steep spectrum outflows and probe regions of thermal absorption. However, in LIRGs the emission detected at 150 MHz does not necessarily come from the main regions of star formation. This implies that high spatial resolution is crucial for accurate estimates of star formation rates for such galaxies at 150 MHz., Comment: 17 pages, 9 figures

Over the last few decades, classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become powerful tools in the study of colloidal fluids. Recently, previous DDFTs for spherically-symmetric particles have been generalised to take into account both inertia and hydrodynamic interactions, two effects which strongly influence non-equilibrium properties. The present work further generalises this framework to systems of anisotropic particles. Starting from the Liouville equation and utilising Zwanzig's projection-operator techniques, we derive the kinetic equation for the Brownian particle distribution function, and by averaging over all but one particle, a DDFT equation is obtained. Whilst this equation has some similarities with DDFTs for spherically-symmetric colloids, it involves a translational-rotational coupling which affects the diffusivity of the (asymmetric) particles. We further show that, in the overdamped (high friction) limit, the DDFT is considerably simplified and is in agreement with a previous DDFT for colloids with arbitrary shape particles., Comment: dynamical density functional theory ; colloidal fluids ; arbitrary-shape particles ; orientable colloids

Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g. Zeldovich-Frenkel or Becker-D\"oring-Tunitskii equations. Starting from a phenomenological stochastic differential equation a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J.F. Lutsko and M.A. Dur\'an-Olivencia, J. Chem. Phys., 2013, 138, 244908] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios. In particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion or interface transfer., Comment: 1 figure

Classical nucleation theory has been recently reformulated based on fluctuating hydrodynamics [J.F. Lutsko and M.A. Dur\'{a}n-Olivencia, J. Chem. Phys. 138, 244908 (2013)]. The present work extends this effort to the case of nucleation in confined systems such as small pores and vesicles. The finite available mass imposes a maximal supercritical cluster size and prohibits nucleation altogether if the system is too small. We quantity the effect of system size on the nuceation rate. We also discuss the effect of relaxing the capillary-model assumption of zero interfacial width resulting in significant changes in the nucleation barrier and nucleation rate., Comment: 16 pages, 4 figures

A two-variable stochastic model for diffusion-limited nucleation is developed using a formalism derived from fluctuating hydrodynamics. The model is a direct generalization of the standard Classical Nucleation Theory. The nucleation rate and pathway are calculated in the weak-noise approximation and are shown to be in good agreement with direct numerical simulations for the weak-solution/strong-solution transition in globular proteins. We find that Classical Nucleation Theory underestimates the time needed for the formation of a critical cluster by two orders of magnitude and that this discrepancy is due to the more complex dynamics of the two variable model and not, as often is assumed, a result of errors in the estimation of the free energy barrier., Comment: 25 pages, 12 figures

In this work a phenomenological stochastic differential equation is proposed to model the time evolution of the radius of a pre-critical molecular cluster during nucleation (the classical order parameter). Such a stochastic differential equation constitutes the basis for the calculation of the (nucleation) induction time under Kramers' theory of thermally activated escape processes. Considering the nucleation stage as a Poisson rare-event, analytical expressions for the induction time statistics are deduced for both steady and unsteady conditions, the latter assuming the semiadiabatic limit. These expressions can be used to identify the underlying mechanism of molecular cluster formation (distinguishing between homogeneous or heterogeneous nucleation from the nucleation statistics is possible) as well as to predict induction times and induction time distributions. The predictions of this model are in good agreement with experimentally measured induction times at constant temperature, unlike the values obtained from the classical equation, but agreement is not so good for induction time statistics. Stochastic simulations truncated to the maximum waiting time of the experiments confirm that this fact is due to the time constraints imposed by experiments. Correcting for this effect, the experimental and predicted curves fit remarkably well. Thus, the proposed model seems to be a versatile tool to predict cluster size distributions, nucleation rates, (nucleation) induction time and induction time statistics for a wide range of conditions (e.g. time-dependent temperature, supersaturation, pH, etc.) where classical nucleation theory is of limited applicability., Comment: 20 pages, 3 figures

It is shown that diffusion-limited classical nucleation theory (CNT) can be recovered as a simple limit of the recently proposed dynamical theory of nucleation based on fluctuating hydrodynamics (Lutsko, JCP 136, 034509 (2012)). The same framework is also used to construct a more realistic theory in which clusters have finite interfacial width. When applied to the dilute solution/dense solution transition in globular proteins, it is found that the extension gives corrections to the the nucleation rate even for the case of small supersaturations due to changes in the monomer distribution function and to the excess free energy. It is also found that the monomer attachement/detachment picture breaks down at high supersaturations corresponding to clusters smaller than about 100 molecules. The results also confirm the usual assumption that most important corrections to CNT can be acheived by means of improved estimates of the free energy barrier. The theory also illustrates two topics that have received considerable attention in the recent literature on nucleation: the importance sub-dominant corrections to the capillary model for the free energy and of the correct choice of the reaction coordinate.