Crossover Time Research Articles

The Value of Initialization on Decadal Timescales: State-Dependent Predictability in the CESM Decadal Prediction Large Ensemble

AbstractInformation in decadal climate prediction arises from a well-initialized ocean state and from the predicted response to an external forcing. The length of time over which the initial conditions benefit the decadal forecast depends on the start date of the forecast. We characterize this state-dependent predictability for decadal forecasts of upper ocean heat content in the Community Earth System Model. We find regionally dependent initial condition predictability, with extended predictability generally observed in the extratropics. We also detect state-dependent predictability, with the year of loss of information from the initialization varying between start dates. The decadal forecasts in the North Atlantic show substantial information from the initial conditions beyond the 10-yr forecast window, and a high degree of state-dependent predictability. We find some evidence for state-dependent predictability in the ensemble spread in this region, similar to that seen in weather and subseasonal-to-seasonal forecasts. For some start dates, an increase of information with lead time is observed, for which the initialized forecasts predict a growing phase of the Atlantic multidecadal oscillation. Finally we consider the information in the forecast from the initial conditions relative to the forced response, and quantify the crossover time scale after which the forcing provides more information. We demonstrate that the climate change signal projects onto different patterns than the signal from the initial conditions. This means that even after the crossover time scale has been reached in a basin-averaged sense, the benefits of initialization can be felt locally on longer time scales.

A model for the jitter of avalanche photodiodes with separate absorption and multiplication regions

An improved version of the Random Path Length algorithm is used to simulate the time response of Separate Absorption and Multiplication Avalanche PhotoDiodes (SAM-APDs) in the linear regime. The model takes into account both the diffusion and the drift of carriers in the absorption region as well as impact ionization scattering events in the multiplication region. An extended formulation of Ramo’s theorem is used to determine the current waveforms. The new algorithm has been used to extract the jitter of the time response of avalanche photodiodes to photons, which is a relevant figure of merit for time of flight applications of SAM-APDs. It is found that an electric field in the absorption region small enough to avoid unwanted carrier multiplication or band-to-band tunneling, is beneficial to reduce the jitter. Furthermore, we have found that, in APDs working in the linear regime, the stochastic duration of the current pulse makes difficult the use of circuit techniques, such as crossover timing, with constant delay lines aimed at detecting the individual pulses. The problem is partly mitigated when SAM-APDs are used for the detection of high energy photons, such as X-rays.

Mpemba effect in molecular gases under nonlinear drag

We look into the Mpemba effect—the initially hotter sample cools sooner—in a molecular gas with nonlinear viscous drag. Specifically, the gas particles interact among them via elastic collisions and with a background fluid at equilibrium. Thus, within the framework of kinetic theory, our gas is described by an Enskog–Fokker–Planck equation. The analysis is carried out using the first Sonine approximation, in which the evolution of temperature is coupled to that of excess kurtosis. This coupling leads to the emergence of the Mpemba effect, which is observed at an early stage of relaxation and when the initial temperatures of the two samples are close enough. This allows for the development of a simple theory, linearizing the temperature evolution around a reference temperature, namely, the initial temperature closer to the asymptotic equilibrium value. The linear theory provides a semiquantitative description of the effect, including expressions for crossover time and maximum temperature difference. We also discuss the limitations of our linearized theory.

Universality and crossover behavior of single-step growth models in 1+1 and 2+1 dimensions.

We study the kinetic roughening of the single-step (SS) growth model with a tunable parameter p in 1+1 and 2+1 dimensions by performing extensive numerical simulations. We show that there exists a very slow crossover from an intermediate regime dominated by the Edwards-Wilkinson class to an asymptotic regime dominated by the Kardar-Parisi-Zhang (KPZ) class for any p<1/2. We also identify the crossover time, the nonlinear coupling constant, and some nonuniversal parameters in the KPZ equation as a function p. The effective nonuniversal parameters are continuously decreasing with p but not in a linear fashion. Our results provide complete and conclusive evidence that the SS model for p≠1/2 belongs to the KPZ universality class in 2+1 dimensions.

Diffusion of DNA-Binding Species in the Nucleus: A Transient Anomalous Subdiffusion Model

Single-particle tracking experiments have measured escape times of DNA-binding species diffusing in living cells: CRISPR-Cas9, TetR, and LacI. The observed distribution is a truncated power law. Working backward from the experimental results, the observed distribution appears inconsistent with a Gaussian distribution of binding energies. Working forward, the observed distribution leads to transient anomalous subdiffusion, in which diffusion is anomalous at short times and normal at long times, here only mildly anomalous. Monte Carlo simulations are used to characterize the time-dependent diffusion coefficient D(t) in terms of the anomalous exponent α, the crossover time tcross, and the limits D(0) and D(∞) and to relate these quantities to the escape time distribution. The simplest interpretations identify the escape time as the actual binding time to DNA or the period of one-dimensional diffusion on DNA in the standard model combining one-dimensional and three-dimensional search, but a more complicated interpretation may be required. The model has several implications for cell biophysics. 1) The initial anomalous regime represents the search of the DNA-binding species for its target DNA sequence. 2) Non-target DNA sites have a significant effect on search kinetics. False positives in bioinformatic searches of the genome are potentially rate-determining in vivo. For simple binding, the search would be speeded if false-positive sequences were eliminated from the genome. 3) Both binding and obstruction affect diffusion. Obstruction ought to be measured directly, using as the primary probe the DNA-binding species with the binding site inactivated and eGFP as a calibration standard among laboratories and cell types. 4) Overexpression of the DNA-binding species reduces anomalous subdiffusion because the deepest binding sites are occupied and unavailable. 5) The model provides a coarse-grained phenomenological description of diffusion of a DNA-binding species, useful in larger-scale modeling of kinetics, FCS, and FRAP.

Domain wall melting in spin-1 XXZ chains

In this letter we study the non-equilibrium spin dynamics in the non-integrable spin-1 XXZ chain, emerging after joining two macroscopic pure states with different magnetizations. Employing the so-called time-dependent variational principle (TDVP) we simulate the dynamics of the total magnetization in the right (left) half of the system up to times that are normally inaccessible by standard tDMRG methods. We identify three distinct phases depending on the anisotropy of the chain, corresponding to diffusive, marginally super-diffusive and insulating. We observe a transient ballistic behaviour with a crossover time that diverges as the isotropic point is approached. We conclude that on intermediate-large time scales the dynamics is well described by the integrable Landau-Lifschitz classical differential equation.

Information growth for sequential monitoring of clinical trials with a stepped wedge cluster randomized design and unknown intracluster correlation.

In a stepped wedge study design, study clusters usually start with the baseline treatment and then cross over to the intervention at randomly determined times. Such designs are useful when the intervention must be delivered at the cluster level and are becoming increasingly common in practice. In these trials, if the outcome is death or serious morbidity, one may have an ethical imperative to monitor the trial and stop before maximum enrollment if the new therapy is proven to be beneficial. In addition, because formal monitoring allows for the stoppage of trials when a significant benefit for new therapy has been ruled out, their use can make a research program more efficient. However, use of the stepped wedge cluster randomized study design complicates the implementation of standard group sequential monitoring methods. Both the correlation of observations introduced by the clustered randomization and the timing of crossover from one treatment to the other impact the rate of information growth, an important component of an interim analysis. We simulated cross-sectional stepped wedge study data in order to evaluate the impact of sequential monitoring on the Type I error and power when the true intracluster correlation is unknown. We studied the impact of varying intracluster correlations, treatment effects, methods of estimating the information growth, and boundary shapes. While misspecified information growth can impact both the Type I error and power of a study in some settings, we observed little inflation of the Type I error and only moderate reductions in power across a range of misspecified information growth patterns in our simulations. Taking the study design into account and using either an estimate of the intracluster correlation from the ongoing study or other data in the same clusters should allow for easy implementation of group sequential methods in future stepped wedge designs.

Clusterization of self-propelled particles in a two-component system.

We consider a mixture of active solute molecules in a suspension of passive solvent particles comprising a thermal bath. The solute molecules are considered to be extended objects with two chemically distinct heads, one head of which having chemical affinity towards the solvent particles. The coupled Langevin equations for the solvent particles along with the equations governing the dynamics of active molecules are numerically simulated to show how the active molecules self-assemble to form clusters which remain in dynamic equilibrium with the free solute molecules. We observe an interesting crossover at an intermediate time in the variation of the order parameter with time when the temperature of the bath is changed signifying the differential behavior of clusterization below and above the crossover time associated with a transition between a thermodynamic and a quasithermodynamic regime. Enthalpy-entropy compensation in the formation of clusters below the crossover is demonstrated.

Cost-Effective Migration Toward Virtualized C-RAN With Scalable Fronthaul Design

Migration from distributed to centralized radio access networks (C-RANs) can be expensive in terms of capital expenditures due to the initial investment while it has lower operational expenditures due to pooling baseband processing into the cloud and reduced power consumption. Partial centralization can be also an option by employing network function splitting and keeping lower physical layer functions colocated with the RUs. This increases the power consumption but relaxes the high capacity requirement in the fronthaul. It is not intuitive which migration strategy is more cost effective. In this article, we formulate a pool placement optimization problem as an integer linear programming (ILP), which minimizes the total cost of ownership (TCO), and evaluate the migration cost to C-RAN with both full centralization of network functions, and partial centralization by using function splitting. We define a network upgrade optimization problem, by adding new cells to the network, as a revisited version of the original optimization problem to evaluate the upgradability of the architectures. We solve the problem with both ILP for optimality, and genetic algorithm for scalability. Simulation results show that partial centralization results in optimal TCO with lower crossover time compared to C-RAN with full centralization.

Langevin Dynamics Study of the Mean Flow Rate-Energy Stochastic Fluid Intrusion Process in Porous Media

Fluid transport phenomena in porous media exhibit different properties with scaling law behavior according to different universal components, which describe the corresponding universal classes exactly. A numerical study of the fluid intrusion process in a porous medium under the effect of a static pressing force is introduced. Investigations are developed by using Langevin dynamic based on the competition between the stochastic and the dissipation processes. The mean flow rate is studied with an energetic study, then the temporal profiles are shown. The results show that the time evolution of these two magnitudes exhibits exponential profiles with two different regimes; transient and permanent, characterized by their cross-over time. They also exhibit a decreasing behavior versus the friction coefficient, but an increasing behavior versus both the static pressure and the medium porosity. Scaling laws with universal exponents of the mean flow rate are checked for different parameters, namely the static pressure and the friction coefficient. The system mean energy follows a scaling law with universal exponents, independently of the parameters (static pressure, friction coefficient, medium porosity, and system size), which proves their universal character.

The effects of extremes and temporal scale on multifractal properties of river flow time series

AbstractFor accurate forecasting of extreme events in rivers, streamflow time series with sub‐daily temporal resolution (1–6 hour) are preferable, but discharge time series for long rivers are usually available at daily or monthly resolution. In this study, the scaling properties of hourly and daily streamflow time series were measured. As an innovation, the effects of extreme values on the multifractal behavior of these series were evaluated. Interestingly, both hourly and daily discharge records led to nearly identical scaling trends and identical crossover times. Daily and hourly discharge time series appeared to be non‐stationary when the timescale ranged from 75 to 366 days. Otherwise, the signals may be considered stationary time series. In addition, the results indicated that the extreme values strongly contribute to the multifractality of the series. The width of singularity spectra decreased considerably when the extreme events were removed from both hourly and daily discharge records.

Implementing a structured model for osteoarthritis care in primary healthcare: A stepped-wedge cluster-randomised trial.

BackgroundTo improve quality of care for patients with hip and knee osteoarthritis (OA), a structured model for integrated OA care was developed based on international recommendations. The objective of this study was to assess the effectiveness of this model in primary care.Methods and findingsWe conducted a cluster-randomised controlled trial with stepped-wedge cohort design in 6 Norwegian municipalities (clusters) between January 2015 and October 2017. The randomised order was concealed to the clusters until the time of crossover from the control to the intervention phase. The intervention was implementation of the SAMBA model, facilitated by interactive workshops for general practitioners and physiotherapists with an update on OA treatment recommendations. Patients in the intervention group attended a physiotherapist-led OA education and individually tailored exercise programme for 8–12 weeks. The primary outcome was patient-reported quality of care (OsteoArthritis Quality Indicator questionnaire; 0–100, 100 = optimal quality) at 6 months. Secondary outcomes included patient-reported referrals to physiotherapy, magnetic resonance imaging (MRI), and orthopaedic surgeon consultation; patients’ satisfaction with care; physical activity level; and proportion of patients who were overweight or obese (body mass index ≥ 25 kg/m2). In all, 40 of 80 general practitioners (mean age [SD] 50 [12] years, 42% females) and 37 of 64 physiotherapists (mean age [SD] 42 [8] years, 65% females) participated. They identified 531 patients, of which 393 patients (mean age [SD] 64 [10] years, 71% females) with symptomatic hip or knee OA were included. Among these, 109 patients were recruited during the control periods (control group), and 284 patients were recruited during interventions periods (intervention group). The patients in the intervention group reported significantly higher quality of care (score of 60 versus 41, mean difference 18.9; 95% CI 12.7, 25.1; p < 0.001) and higher satisfaction with OA care (odds ratio [OR] 12.1; 95% CI 6.44, 22.72; p < 0.001) compared to patients in the control group. The increase in quality of care was close to, but below, the pre-specified minimal important change. In the intervention group, a higher proportion was referred to physiotherapy (OR 2.5; 95% CI 1.08, 5.73; p = 0.03), a higher proportion fulfilled physical activity recommendations (OR 9.3; 95% CI 2.87, 30.37; p < 0.001), and a lower proportion was referred to an orthopaedic surgeon (OR 0.3; 95% CI 0.08, 0.80; p = 0.02), as compared to the control group. There were no significant group differences regarding referral to MRI (OR 0.6; 95% CI 0.13, 2.38; p = 0.42) and proportion of patients who were overweight or obese (OR 1.3; 95% CI 0.70, 2.51; p = 0.34). Study limitations include the imbalance in patient group size, which may have been due to an increased attention to OA patients among the health professionals during the intervention phase, and a potential recruitment bias as the patient participants were identified by their health professionals.ConclusionsIn this study, a structured model in primary care resulted in higher quality of OA care as compared to usual care. Future studies should explore ways to implement the structured model for integrated OA care on a larger scale.Trial registrationClinicalTrials.gov NCT02333656.

Crossover from anomalous to Fickean behavior in infiltration and reaction in fractal porous media

When the solution in a porous medium is in chemical equilibrium with mineral grains and an external surface is put in contact with water, the infiltration of unsaturated solution may be accompanied by mineral reactions that change the morphology of that medium. Here we study the evolution of this infiltration process considering that the initial porous media are fractal and that the reactions form additional porous material plus soluble products. A Sierpinski carpet and a Menger sponge are the fractal models, the mineral inclusions are represented by the non-fractal blocks (squares and cubes) formed in their iterative constructions, and reaction rates are described by a thermally activated model, in conditions of slow reactions in comparison with the diffusion. The interplay between the infiltration by diffusion and the structural changes by the reactions is explained by a combination of kinetic Monte Carlo simulations of lattice models and a scaling approach. At short times, the infiltration is subdiffusive, but the dissolved mass increases anomalously fast due to delocalization of the reaction, which is distributed through a time increasing infiltrated region. At long times, normal (Fickean) infiltration and reaction are observed. The crossover between the two regimes occurs when the thickness of the altered layer formed around the mineral inclusions is of the same order of magnitude of the width a of the smallest gaps between those inclusions. The order of magnitude of the crossover time tc is estimated as a/(vk), where k is the reaction rate constant and v is the molar volume of the mineral; this time does not depend on the diffusion coefficient of reaction products or on the fractal geometry of the initial medium, which suggests the application to a variety of systems. Estimates of tc are obtained in two recently studied rocks with reported fractal properties and justify the Fickean diffusion assumption of previous models for their weathering in geological time scales. The morphological evolution of the mineral blocks that partially reacted qualitatively agrees with experiments.

Polymerization Induces Non-Gaussian Diffusion

Recent theoretical modeling offers a unified picture for the description of stochastic processes characterized by a crossover from anomalous to normal behavior. This is particularly welcome, as a growing number of experiments suggest the crossover to be a common feature shared by many systems: in some cases the anomalous part of the dynamics amounts to a Brownian yet non-Gaussian diffusion; more generally, both the diffusion exponent and the distribution may deviate from normal behavior in the initial part of the process. Since proposed theories work at a mesoscopic scale invoking the subordination of diffusivities, it is of primary importance to bridge these representations with a more fundamental, ``microscopic'' description. We argue that the dynamical behavior of macromolecules during simple polymerization processes provide suitable setups in which analytic, numerical, and particle-tracking experiments can be contrasted at such a scope. Specifically, we demonstrate that Brownian yet non-Gaussian diffusion of the center of mass of a polymer is a direct consequence of the polymerization process. Through the kurtosis, we characterize the early-stage non-Gaussian behavior within a phase diagram, and we also put forward an estimation for the crossover time to ordinary Brownian motion.

Transient Anomalous Diffusion in Run-and-Tumble Dynamics

We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain the current direction of motion. We consider a run-and-tumble process, which is a combination of an active fast motility mode (persistent motion) and a passive slow mode (diffusion). Assuming stochastic transitions between the two motility states, we derive an analytical expression for the time evolution of the mean square displacement. The interplay of the key parameters and the initial conditions as for instance the probability of initially starting in the run or tumble state leads to a variety of transient regimes of anomalous transport on different time scales before approaching the asymptotic diffusive dynamics. We estimate the crossover time to the long-term diffusive regime and prove that the asymptotic diffusion constant is independent of initially starting in the run or tumble state.

Random walks on intersecting geometries.

We present an analytical approach to study simple symmetric random walks on a crossing geometry consisting of a plane square lattice crossed by n_{l} number of lines that all meet each other at a single point (the origin) on the plane. The probability density to find the walker at a given distance from the origin either in a line or in the plane geometry is exactly calculated as a function of time t. We find that the large-time asymptotic behavior of the walker for any arbitrary number n_{l} of lines is eventually governed by the diffusion of the walker on the plane after a crossover time approximately given by t_{c}∝n_{l}^{2}. We show that this competition can be changed in favor of the line geometry by switching on an arbitrarily small perturbation of a drift term in which even a weak biased walk is able to drain the whole probability density into the line at long-time limit. We also present the results of our extensive simulations of the model which perfectly support our analytical predictions. Our method can, however, be simply extended to other crossing geometries with a single common point.

One Year Follow-up of a Randomized, Double-Blind, Placebo-Controlled Trial of Percutaneous Peripheral Nerve Stimulation for Chronic Neuropathic Pain Following Amputation

Abstract INTRODUCTION Over 85% of patients experience residual limb (RLP) and/or phantom limb (PLP) pain following amputation. Peripheral nerve stimulation (PNS) is a non-opioid approach to relieve postamputation neuropathic pain. A recent multicenter, randomized, double-blind, placebo-controlled study using a novel percutaneous PNS system demonstrated clinically and statistically significant improvements in pain and pain interference with PNS compared to placebo (Gilmore et al, 2019). This work presents prospective 1-yr follow-up to assess durability of pain relief and functional improvements. METHODS Over 85% of patients experience residual limb (RLP) and/or phantom limb (PLP) pain following amputation. Peripheral nerve stimulation (PNS) is a non-opioid approach to relieve post-amputation neuropathic pain. A recent multicenter, randomized, double-blind, placebo-controlled study using a novel percutaneous PNS system demonstrated clinically and statistically significant improvements in pain and pain interference with PNS compared to placebo (Gilmore et al, 2019). This work presents prospective one-year follow-up to assess durability of pain relief and functional improvements. RESULTS A significantly greater proportion of subjects who completed the 12-mo visit reported = 50% pain relief on the BPI-SF (5/8, 63%; average pain relief = 73% among responders) compared to the placebo group at the time of crossover (0/14, 0%, P = .003; average pain relief = 23%). A majority of subjects also reported = 50% reductions in pain interference at 12 mo (5/8, 63%). Two of 13 (15%) subjects in the placebo group reported sustained improvements in pain interference (P = .06). Average reduction in pain interference among responders in the PNS group was 87%. CONCLUSION This work suggests that PNS delivered over 60 d may provide clinically significant and enduring pain relief, enabling improved function and potentially reducing the need for a permanently implanted system.

An investigation of listener envelopment utilizing a spherical microphone array and third-order ambisonics reproduction.

Listener envelopment (LEV), the sense of being surrounded by the sound field, is a perception that has been found to be related to the overall impression of a concert hall. The purpose of this study was to investigate the relationship between the perception of LEV and the direction and arrival time of energy from spatial room impulse responses (IRs). IRs were obtained in a 2000-seat concert hall using a 32-channel spherical microphone array and analyzed using a third-order plane wave decomposition. Additionally, the IRs were convolved with anechoic music and processed for third-order Ambisonic reproductions and presented to subjects over a 30-loudspeaker array. Instances were found in which the energy in the late sound field did not correlate with LEV ratings as well as energy in a 70-100 ms time window. Follow-up listening tests were conducted with hybrid IRs containing portions of an enveloping IR and an unenveloping IR with crossover times ranging from 40 to 140 ms. Additional hybrid IRs were studied wherein portions of the spatial IRs were collapsed into all frontal energy with crossover times ranging from 40 to 120 ms. The tests confirmed that much of the important LEV information exists in the early portion of these IRs.

Mobility of Polymer-Tethered Nanoparticles in Unentangled Polymer Melts.

A scaling theory is developed for the motion of a polymer-tethered nanoparticle (NP) in an unentangled polymer melt. We identify two types of scaling regimes depending on the NP diameter d and the size of a grafted polymer chain (tail) R tail . In one type of regimes, the tethered NP motion is dominated by the bare NP, as the friction coefficient of the tails is lower than that of the less mobile particle. The time dependence of the mean square displacement (MSD) of the tethered NP ⟨Δr 2(t)⟩ in the particle-dominated regime can be approximated by ⟨Δr 2(t)⟩ bare for the bare NP. In the other type of regimes, the tethered NP motion is dominated by the tails when the friction coefficient of the tails surpasses that of the particle at times longer than the crossover time τ ∗. In a tail-dominated regime, the MSD ⟨Δr 2(t)⟩ ≈ ⟨Δr 2(t)⟩ bare only for t < τ ∗. ⟨Δr 2(t)⟩ of a single-tail NP for t > τ ∗ is approximated as the MSD ⟨Δr 2(t)⟩ tail of monomers in a free tail, whereas ⟨Δr 2(t)⟩ of a multi-tail NP for t > τ ∗ is approximated as the MSD ⟨Δr 2(t)⟩ star of the branch point of a star polymer. The time dependence of ⟨Δr 2(t)⟩ in a tail-dominated regime exhibits two qualitatively different sub-diffusive regimes. The first sub-diffusive regime for t < τ ∗ arises from the dynamical coupling between the particle and the melt chains. The second sub-diffusive regime for t > τ ∗ occurs as the particle participates in the dynamics of the tails. For NPs with loosely grafted chains, there is a Gaussian brush region surrounding the NP, where the chain strands in Gaussian conformations undergo Rouse dynamics with no hydrodynamic coupling. The crossover time τ ∗ for loosely grafted multi-tail NPs in a tail-dominated regime decreases as the number of tails increases. For NPs with densely grafted chains, the tails are hydrodynamically coupled to each other. The hydrodynamic radii for the diffusion of densely grafted multi-tail NPs are approximated by the sum of the particle and tail sizes.

Long-term physical evolution of an elastomeric ultrasound contrast microbubble

HypothesisOne of the main assets of crosslinked polymer-shelled microbubbles (MBs) as ultrasound-active theranostic agents is the robustness of the shells, combined with the chemical versatility in modifying the surface with ligands and/or drugs. Despite the long shelf-life, subtle modifications occur in the MB shells involving shifts in acoustic, mechanical and structural properties. ExperimentsWe carried out a long-term morphological and acoustic evolution analysis on elastomeric polyvinyl-alcohol (PVA)-shelled MBs, a novel platform accomplishing good acoustic and surface performances in one agent. Confocal laser scanning microscopy, acoustic spectroscopy and AFM nanomechanics were integrated to understand the mechanism of PVA MBs ageing. The changes in the MB acoustic properties were framed in terms of shell thickness and viscoelasticity using a linearised oscillation theory, and compared to MB morphology and to nanomechanical analysis. FindingsWe enlightened a novel, intriguing ageing time evolution of the PVA MBs with double behaviour with respect to a crossover time of ∼50 days. Before, significant changes occur in MB stiffness and shell thickness, mainly due to a massive release of entangled PVA chains. Then, the MB resonance frequency increases together with shell thickening and softening. Our benchmark study is of general interest for emerging viscoelastomeric bubbles towards personalised medicine.