Forecasting with an N-dimensional Langevin equation and a neural-ordinary differential equation.

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 naïve methods.

Comparative analysis of antiproliferative and vasodilator effects of drugs for pulmonary hypertension: Extensive in vitro study in rats and human.

An effective pulmonary hypertension (PH) treatment should combine antiproliferative and vasodilator effects. We characterized a wide-range of drugs comparing their anti-proliferative vs vasodilator effects in human and rat pulmonary artery smooth muscle cells (PASMC). Key findings: 1) Approved PH drugs (PDE5 inhibitors, sGC stimulators and PGI2 agonists) are preferential vasodilators. 2) cGMP stimulators were more effective in cells derived from hypertensive rats. 3) Nifedipine acted equally as vasodilator and antiproliferative. 4) quercetin and imatinib were potent dual vasodilator/antiproliferative drugs. 5) Tacrolimus and levosimendan lacked antiproliferative effects. 6) Forskolin, pinacidil and hydroxyfasudil were more effective as antiproliferative in human cells.

Physics-informed Bayesian inference of external potentials in classical density-functional theory.

The swift progression and expansion of machine learning (ML) have not gone unnoticed within the realm of statistical mechanics. In particular, ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable automatic discovery of free-energy functionals to determine the equilibrium-density profile of a many-particle system. Within classical 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 classical 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 classical 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 characterize 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, wetting, and capillarity, to name a few.

Vitamin D Receptor Deficiency Upregulates Pulmonary Artery Kv7 Channel Activity.

Recent evidence suggests that vitamin D is involved in the development of pulmonary arterial hypertension (PAH). The aim of this study was to analyze the electrophysiological and contractile properties of pulmonary arteries (PAs) in vitamin D receptor knockout mice (Vdr-/-). PAs were dissected and mounted in a wire myograph. Potassium membrane currents were recorded in freshly isolated PA smooth muscle cells (PASMCs) using the conventional whole-cell configuration of the patch-clamp technique. Potential vitamin D response elements (VDREs) in Kv7 channels coding genes were studied, and their protein expression was analyzed. Vdr-/- mice did not show a pulmonary hypertensive phenotype, as neither right ventricular hypertrophy nor endothelial dysfunction was apparent. However, resistance PA from these mice exhibited increased response to retigabine, a Kv7 activator, compared to controls and heterozygous mice. Furthermore, the current sensitive to XE991, a Kv7 inhibitor, was also higher in PASMCs from knockout mice. A possible VDRE was found in the gene coding for KCNE4, the regulatory subunit of Kv7.4. Accordingly, Vdr-/- mice showed an increased expression of KCNE4 in the lungs, with no changes in Kv7.1 and Kv7.4. These results indicate that the absence of Vdr in mice, as occurred with vitamin D deficient rats, is not sufficient to induce PAH. However, the contribution of Kv7 channel currents to the regulation of PA tone is increased in Vdr-/- mice, resembling animals and humans suffering from PAH.

Hydrogen sulfide regulates the redox state of soluble guanylate cyclase in CSE-/- mice corpus cavernosum microcirculation.

The corpus cavernosum (CC) is a highly vascularized tissue and represents an excellent example of microcirculation. Indeed, erectile dysfunction is considered an early index of cardiovascular disease. Hydrogen sulfide (H2S) at the vascular level is endogenously produced from L-cysteine mainly by the action of cystathionine-γ-lyase (CSE) and plays a role in CC vascular homeostasis. Here we have evaluated the involvement of the endogenous H2S in the regulation of the soluble guanylate cyclase (sCG) redox state. The lack of CSE-derived endogenous H2S, in CSE-/- mice, disrupted the eNOS/NO/sGC/PDE pathway. Indeed, the absence of CSE-derived endogenous H2S caused a significant reduction of the relaxant response to riociguat, an sGC redox-dependent stimulator. Conversely, the response to cinaciguat, an sGC redox-independent activator, was not modified. The relevance of the role played at the redox level of the endogenous H2S was confirmed by the findings that in CC harvested from CSE-/- mice there was a significant reduction of GCß1 expression coupled with a decrease in CYP5R3, a reductase involved in the regulation of the redox state of sGC. These molecular changes driven by the lack of endogenous H2S translate into a significant reduction in cGMP levels. The replenishment of the lack of H2S with an H2S donor rescued the relaxant response to riociguat in CC of CSE-/- mice. In conclusion, the endogenous CSE-derived H2S plays a physiological key role in the regulation of the redox state of sGC in CC microcirculation.

Oxidized soluble guanylyl cyclase causes erectile dysfunction in alcoholic mice.

BACKGROUND AND PURPOSE: Alcohol abuse has been associated with erectile dysfunction (ED), but the implicated molecular mechanisms are unresolved. This study analyses the role of alterations in soluble guanylyl cyclase (sGC) in ED. EXPERIMENTAL APPROACH: ED was analysed in adult male C57BL/6J mice subjected to the Chronic Intermittent Ethanol (CIE) paradigm. Erectile function was assessed in anaesthetised mice in vivo by evaluating intracavernosal pressure (ICP) and in vitro in isolated mice corpora cavernosa (CC) mounted in a myograph. Protein expression and reactive oxygen species were analysed by western blot and dihydroethidium staining, respectively. KEY RESULTS: In CIE mice, we observed a significant decrease in the relaxant response of the CC to stimulation of NO release from nitrergic nerves by electrical field stimulation, to NO release from endothelial cells by acetylcholine, to the PDE5 inhibitor sildenafil, and to the sGC stimulator riociguat. Conversely, the response to the sGC activator cinaciguat, whose action is independent of the oxidation state of sGC, was significantly enhanced in these CC. The responses to adenylyl cyclase stimulation with forskolin were unchanged. We found an increase in reactive oxygen species in the CC from CIE mice as well as an increase in CYP2E1 and NOX2 protein expression. In vivo pre-treatment with tempol prevented alcohol-induced erectile dysfunction. CONCLUSIONS AND IMPLICATIONS: Our results demonstrate that alcoholic mice show ED in vitro and in vivo due to an alteration in the redox state of sGC and suggest that sGC activators may be effective in ED associated with alcoholism.

Machine Learning Memory Kernels as Closure for Non-Markovian Stochastic Processes.

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, 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 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 nonequilibrium processes opening also a new route for stochastic modeling.

Understanding Soaring Coronavirus Cases and the Effect of Contagion Policies in the UK.

The number of new daily SARS-CoV-2 infections experienced an abrupt increase during the last quarter of 2020 in almost every European country. The phenomenological explanation offered was a new mutation of the virus, first identified in the UK. We use publicly available data in combination with a time-delayed controlled SIR model, which captures the effects of preventive measures on the spreading of the virus. We are able to reproduce the waves of infection occurred in the UK with a unique transmission rate, suggesting that the new SARS-CoV-2 variant is as transmissible as previous strains. Our findings indicate that the sudden surge in cases was, in fact, related to the relaxation of preventive measures and social awareness. We also simulate the combined effects of restrictions and vaccination campaigns in 2021, demonstrating that lockdown policies are not fully effective to flatten the curve. For effective mitigation, it is critical that the public keeps on high alert until vaccination reaches a critical threshold.

KV 1.3 channels are novel determinants of macrophage-dependent endothelial dysfunction in angiotensin II-induced hypertension in mice.

BACKGROUND AND PURPOSE: KV 1.3 channels are expressed in vascular smooth muscle cells (VSMCs), where they contribute to proliferation rather than contraction and participate in vascular remodelling. KV 1.3 channels are also expressed in macrophages, where they assemble with KV 1.5 channels (KV 1.3/KV 1.5), whose activation generates a KV current. In macrophages, the KV 1.3/KV 1.5 ratio is increased by classical activation (M1). Whether these channels are involved in angiotensin II (AngII)-induced vascular remodelling, and whether they can modulate the macrophage phenotype in hypertension, remains unknown. We characterized the role of KV 1.3 channels in vascular damage in hypertension. EXPERIMENTAL APPROACH: We used AngII-infused mice treated with two selective KV 1.3 channel inhibitors (HsTX[R14A] and [EWSS]ShK). Vascular function and structure were measured using wire and pressure myography, respectively. VSMC and macrophage electrophysiology were studied using the patch-clamp technique; gene expression was analysed using RT-PCR. KEY RESULTS: AngII increased KV 1.3 channel expression in mice aorta and peritoneal macrophages which was abolished by HsTX[R14A] treatment. KV 1.3 inhibition did not prevent hypertension, vascular remodelling, or stiffness but corrected AngII-induced macrophage infiltration and endothelial dysfunction in the small mesenteric arteries and/or aorta, via a mechanism independent of electrophysiological changes in VSMCs. AngII modified the electrophysiological properties of peritoneal macrophages, indicating an M1-like activated state, with enhanced expression of proinflammatory cytokines that induced endothelial dysfunction. These effects were prevented by KV 1.3 blockade. CONCLUSIONS AND IMPLICATIONS: We unravelled a new role for KV 1.3 channels in the macrophage-dependent endothelial dysfunction induced by AngII in mice which might be due to modulation of macrophage phenotype.

Uncovered Contribution of Kv7 Channels to Pulmonary Vascular Tone in Pulmonary Arterial Hypertension.

K+ channels play a fundamental role regulating membrane potential of pulmonary artery (PA) smooth muscle cells and their impairment is a common feature in pulmonary arterial hypertension (PAH). K+ voltage-gated channel subfamily Q (KCNQ1-5) or Kv7 channels and their regulatory subunits subfamily E (KCNE) regulatory subunits are known to regulate vascular tone, but whether Kv7 channel function is impaired in PAH and how this can affect the rationale for targeting Kv7 channels in PAH remains unknown. Here, we have studied the role of Kv7/KCNE subunits in rat PA and their possible alteration in PAH. Using the patch-clamp technique, we found that the total K+ current is reduced in PA smooth muscle cells from pulmonary hypertension animals (SU5416 plus hypoxia) and Kv7 currents made a higher contribution to the net K+ current. Likewise, enhanced vascular responses to Kv7 channel modulators were found in pulmonary hypertension rats. Accordingly, KCNE4 subunit was highly upregulated in lungs from pulmonary hypertension animals and patients. Additionally, Kv7 channel activity was enhanced in the presence of Kv1.5 and TASK-1 channel inhibitors and this was associated with an increased KCNE4 membrane abundance. Compared with systemic arteries, PA showed a poor response to Kv7 channel modulators which was associated with reduced expression and membrane abundance of Kv7.4 and KCNE4. Our data indicate that Kv7 channel function is preserved and KCNE4 is upregulated in PAH. Therefore, compared with other downregulated channels, the contribution of Kv7 channels is increased in PAH resulting in an enhanced sensitivity to Kv7 channel modulators. This study provides insight into the potential usefulness of targeting Kv7 channels in PAH.

Total, Bioavailable, and Free Vitamin D Levels and Their Prognostic Value in Pulmonary Arterial Hypertension.

Introduction: Epidemiological studies suggest a relationship between vitamin D deficiency and cardiovascular and respiratory diseases. However, whether total, bioavailable, and/or free vitamin D levels have a prognostic role in pulmonary arterial hypertension (PAH) is unknown. We aimed to determine total, bioavailable, and free 25-hydroxy-vitamin D (25(OH)vitD) plasma levels and their prognostic value in PAH patients. Methods: In total, 67 samples of plasma from Spanish patients with idiopathic, heritable, or drug-induced PAH were obtained from the Spanish PH Biobank and compared to a cohort of 100 healthy subjects. Clinical parameters were obtained from the Spanish Registry of PAH (REHAP). Results: Seventy percent of PAH patients had severe vitamin D deficiency (total 25(OH)vitD < 10 ng/mL) and secondary hyperparathyroidism. PAH patients with total 25(OH)vitD plasma above the median of this cohort (7.17 ng/mL) had better functional class and higher 6-min walking distance and TAPSE (tricuspid annular plane systolic excursion). The main outcome measure of survival was significantly increased in these patients (age-adjusted hazard ratio: 5.40 (95% confidence interval: 2.88 to 10.12)). Vitamin D-binding protein (DBP) and albumin plasma levels were downregulated in PAH. Bioavailable 25(OH)vitD was decreased in PAH patients compared to the control cohort. Lower levels of bioavailable 25(OH)vitD (<0.91 ng/mL) were associated with more advanced functional class, lower exercise capacity, and higher risk of mortality. Free 25(OH)vitD did not change in PAH; however, lower free 25(OH)vitD (<1.53 pg/mL) values were also associated with high risk of mortality. Conclusions: Vitamin D deficiency is highly prevalent in PAH, and low levels of total 25(OH)vitD were associated with poor prognosis.

Macroscopic relations for microscopic properties at the interface between solid substrates and dense fluids.

Strongly confined fluids exhibit inhomogeneous properties due to atomistic structuring in close proximity to a solid surface. State variables and transport coefficients at a solid-fluid interface vary locally and become dependent on the properties of the confining walls. However, the precise mechanisms for these effects are not known as of yet. Here, we make use of nonequilibrium molecular dynamics simulations to scrutinize the local fluid properties at the solid-fluid interface for a range of surface conditions and temperatures. We also derive microscopic relations connecting fluid viscosity and density profiles for dense fluids. Moreover, we propose empirical ready-to-use relations to express the average density and viscosity in the channel as a function of temperature, wall interaction strength, and bulk density or viscosity. Such relations are key to technological applications such as micro-/nanofluidics and tribology but also natural phenomena.

Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations.

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, as opposed to the perfectly uncorrelated limit studied by Grün et al. (J Stat Phys 122(6):1261-1291, 2006). We also present a numerical scheme based on a spectral collocation method, which is then utilised to simulate the stochastic thin-film equation. This scheme seems to be very convenient for numerical studies of the stochastic thin-film equation, since it makes it easier to select the frequency modes of the noise (following the spirit of the long-wave approximation). With our numerical scheme we explore the fluctuating dynamics of the thin film and the behaviour of its free energy in the vicinity of rupture. Finally, we study the effect of the noise intensity on the rupture time, using a large number of sample paths as compared to previous studies.

Step Crowding Effects Dampen the Stochasticity of Crystal Growth Kinetics.

Crystals grow by laying down new layers of material which can either correspond in size to the height of one unit cell (elementary steps) or multiple unit cells (macrosteps). Surprisingly, experiments have shown that macrosteps can grow under conditions of low supersaturation and high impurity density such that elementary step growth is completely arrested. We use atomistic simulations to show that this is due to two effects: the fact that the additional layers bias fluctuations in the position of the bottom layer towards growth and by a transition, as step height increases, from a 2D to a 3D nucleation mechanism.

Unification of classical nucleation theories via a unified Itô-Stratonovich stochastic equation.

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-Döring-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. Durán-Olivencia, J. Chem. Phys. 138, 244908 (2013)10.1063/1.4811490] 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.

A two-parameter extension of classical nucleation theory.

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 (CNT). 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 CNT 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.

Mesoscopic nucleation theory for confined systems: a one-parameter model.

Classical nucleation theory has been recently reformulated based on fluctuating hydrodynamics [J. F. Lutsko and M. A. Durán-Olivencia, Classical nucleation theory from a dynamical approach to nucleation, 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 nucleation 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.

Observing classical nucleation theory at work by monitoring phase transitions with molecular precision.

It is widely accepted that many phase transitions do not follow nucleation pathways as envisaged by the classical nucleation theory. Many substances can traverse intermediate states before arriving at the stable phase. The apparent ubiquity of multi-step nucleation has made the inverse question relevant: does multistep nucleation always dominate single-step pathways? Here we provide an explicit example of the classical nucleation mechanism for a system known to exhibit the characteristics of multi-step nucleation. Molecular resolution atomic force microscopy imaging of the two-dimensional nucleation of the protein glucose isomerase demonstrates that the interior of subcritical clusters is in the same state as the crystalline bulk phase. Our data show that despite having all the characteristics typically associated with rich phase behaviour, glucose isomerase 2D crystals are formed classically. These observations illustrate the resurfacing importance of the classical nucleation theory by re-validating some of the key assumptions that have been recently questioned.

Classical nucleation theory from a dynamical approach to nucleation.

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 [J. F. Lutsko, J. Chem. Phys. 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 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 attachment/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 achieved 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.