Continuous-time Analysis Research Articles

Impact of Time of Day on Surgical Outcomes After Lung Transplantation (Night-Time Lung Transplant)

BackgroundSurgical outcomes have been linked to the technical and cognitive abilities of an exhausted surgical team. In parallel, advancements in preservation have led to the proposal of daytime lung transplants. We sought to investigate whether time of day is associated with outcomes in lung transplants. MethodsData on 30,404 lung transplants from 2005 to 2021 were obtained from the United Network for Organ Sharing database. Patients were categorized based on the time of surgery with early-hours defined as donor cross-clamp between 10 pm and 3 am, and Cox regression models for 90-day and long-term mortality were made to assess the risk according to time of transplant and covariates. Additionally, the Cox modeling was repeated with donor cross-clamp and the estimated reperfusion time of day as continuous functions. ResultsAmong 30,404 transplants, 20.7% (6295) were performed during early hours. No significant difference was found between the 2 groups in unadjusted 90-day and long-term mortality (log-rank, P = .176 and .363, respectively), and results were unchanged when adjusting for covariates (P = .233 and .738, respectively). However, when examining donor cross-clamp time and reperfusion time as continuous variables in separate multivariable analyses, we observed significant associations with 90-day mortality (P = .002 and .022, respectively). Notably, lower mortality rates were observed for donor clamp-times between 8 am and 1 pm and estimated reperfusion times between 1 pm and 6 pm. ConclusionsAlthough binary categorizations of the time of day of lung transplants did not show a significant impact on short- or long-term survival, continuous-time analyses demonstrated that certain times during the day were associated with favorable short-term survival.

The Innate Rates of Increase in Two Common Stored Grain Insects under Different Grain Storage Conditions and Times.

The determination of innate rate of increase (r) values under different grain storage conditions is critical for insect population predictions. The r values for Cryptolestes ferrugineus (Stephens) and Tribolium castaneum (Herbst) were calculated by using a new suggested method (continuous time analysis) and data from the literature, and these calculated r values were compared to identify the r values and carrying capacities under real grain storage conditions and times. The insects were reared in small glass vials (0.3 kg wheat), small PVC columns (2 kg wheat), large PVC columns (14 kg wheat), and shallow containers (14 kg wheat or wheat + cracked wheat). The wheat or cracked wheat had 13.8 to 14.5% moisture contents at different constant temperatures (17.5 to 42.5 °C) and fluctuating temperatures. The r values at the beginning of the population were the highest. Before r became negative, it gradually decreased with increasing time. After the r value became negative, it sometimes increased to positive; however, the rebounded r was much less than the initial r and gradually tended to stabilize within an up-and-down range. This up-and-down r was related to the carrying capacity. The larger the grain bulk, the higher the innate rate was for both species. The r values associated with 14 kg of wheat could be used to predict the insect population dynamics in stored grain bins.

Budget Deficit in a Growing Economy and Impossibility of Fiscal Collapse: A Continuous Time Analysis

Abstract Using a continuous time dynamic model of growing economy we will show the following results. 1) When people derive utility from their money holding (or government bond holding) along with their consumption, a budget deficit is essential to achieve and maintain full employment under stable prices or inflation in a growing economy. 2) If we take into account that government spending due to budget deficits increases financial assets held by the private sector, and then consumption will occur from assets in addition to consumption from income, even when the interest rate on government bonds is higher than the real economic growth rate, the ratio of government debt to GDP can not diverge and the divergence is naturally prevented by mild inflation. The required inflation rate is such that the interest rate of the government bonds is smaller than the weighted average of the rate of return on capital and the nominal growth rate. Since the interest rate of the government bonds is usually considered smaller than the rate of return on capital, this is not a very demanding requirement. Thus, we need not worry at all about the accumulation of government debt or about the divergence of the debt to GDP ratio, which is often taken as an indicator of fiscal collapse.

Budget deficit in a growing economy and impossibility of fiscal collapse: a continuous time analysis

Budget deficit in a growing economy and impossibility of fiscal collapse: a continuous time analysis

Stochastic Gradient Descent with Noise of Machine Learning Type Part II: Continuous Time Analysis

Stochastic Gradient Descent with Noise of Machine Learning Type Part II: Continuous Time Analysis

A Functional Data Approach for Continuous-Time Analysis Subject to Modeling Discrepancy under Infill Asymptotics

Parametric continuous-time analysis often entails derivations of continuous-time models from predefined discrete formulations. However, undetermined convergence rates of frequency-dependent parameters can result in ill-defined continuous-time limits, leading to modeling discrepancy, which impairs the reliability of fitting and forecasting. To circumvent this issue, we propose a simple solution based on functional data analysis (FDA) and truncated Taylor series expansions. It is demonstrated through a simulation study that our proposed method is superior—compared with misspecified parametric methods—in fitting and forecasting continuous-time stochastic processes, while the parametric method slightly dominates under correct specification, with comparable forecast errors to the FDA-based method. Due to its generally consistent and more robust performance against possible misspecification, the proposed FDA-based method is recommended in the presence of modeling discrepancy. Further, we apply the proposed method to predict the future return of the S&P 500, utilizing observations extracted from a latent continuous-time process, and show the practical efficacy of our approach in accurately discerning the underlying dynamics.

The quest to develop automated systems for monitoring animal behavior

Automated behavior analysis (ABA) strategies are being researched at a rapid rate to detect an array of behaviors across a range of species. There is growing optimism that soon ethologists will not have to manually decode hours (and hours) of animal behavior videos, but that instead computers will process them for us. However, before we assume ABA is ready for practical use, it is important to take a realistic look at exactly what ABA is being developed, the expertise being used to develop it, and the context in which these studies occur. Once we understand common pitfalls occurring during ABA development and identify limitations, we can construct robust ABA tools to achieve automated (ultimately even continuous and real time) analysis of behavioral data, allowing for more detailed or longer-term studies of behavior on larger numbers of animals than ever before. ABA is only as good as it is trained to be. A key starting point is having manually annotated data for model training and assessment. However, most ABA developers are not trained in ethology. Often no formal ethogram is developed and descriptions of target behaviors in ABA publications are limited or inaccurate. In addition, ABA is also frequently developed using small datasets, which lack sufficient variability in animal morphometrics, activities, camera viewpoints, and environmental features to be generalizable. Thus, ABA often needs to be further validated before being used satisfactorily on different populations or under other conditions, even for research purposes. Multidisciplinary teams of researchers including ethologists and ethicists as well as computer scientists, data scientists, and engineers are needed to help address problems when applying computer vision ABA to measure behavior. Reference datasets that can be used for behavior detection should be generated and shared that include image data, annotations, and baseline analyses for benchmarking. Also critical is the development of standards for creating such reference datasets and descriptions of best practices for methods for validating results from detection tools to ensure they are robust and generalizable. At present, only a handful of publicly available datasets exist that can be used for development of ABA tools. As we work to realize the promise of ABA (and subsequent precision livestock farming technologies) to detect animal behavior, a clear understanding of best practices, access to accurately annotated datasets, and networking among ethologists and ABA developers will increase our chances for rapid and robust successes.

The Inherent Instability of Environmental Parameters Governing Indoor Air Quality on Board Ships and the Use of Temporal Trends to Identify Pollution Sources

Indoor air quality on board a 36-year-old ship has been characterized at several locations. The ship is dedicated to nearshore operations at the Belgian coast. This paper presents time-averaged and continuous-time measurements of several indoor pollutant concentrations such as NO2, O3, NO, CO, total volatile organic compounds (TVOC), polycyclic aromatic hydrocarbons (PAH), particulate matter PM2.5 and PM10, black carbon, and individual organic compounds. Time-averaged measurements suggest that the ship’s indoor air quality is sufficiently safe according to the prescribed occupational and nonoccupational health limits. However, the concentration of some indoor pollutants is comparable to that of the outdoor air of a large city such as Brussels, Belgium. Continuous-time analyses show that the temporal trends of indoor pollutant concentrations are inherently unstable. A large number of peaks or valleys are observed on a slowly fluctuating background. At some occasions, pollutant concentrations exceed the nonoccupational thresholds. Several pollutant peaks occur simultaneously, resulting in a pattern of peaks that is typical for a pollution source (e.g., exhaust gases entering the ship’s castle through the ventilation inlet, human presence, and bunkering). This study illustrates that multiparameter monitoring campaigns give valuable information about the behaviour of pollution sources, facilitating the definition of mitigation actions.

Day-to-day coordination of the stress and reproductive axes: A continuous-time analysis of within-person testosterone and cortisol relationships in athletic and healthy men

Day-to-day coordination of the stress (i.e., hypothalamic-pituitary-adrenal [HPA]) and reproductive (i.e., hypothalamic-pituitary-gonadal [HPG]) axes is central to allostatic regulation, reproductive success, and survival. Reports of positive, within-person testosterone and cortisol relationships (or coupling) suggest cross-talk of a facilitative nature, but longitudinal evidence is scarce and has methodological and analytical limitations. To address this, we used a continuous-time (CT) model to investigate day-to-day, within-person coupling of testosterone and cortisol in two male cohorts. Salivary testosterone and cortisol fluctuations were monitored in 35 athletic men across two international tournaments (M = 19.3 tests) and in 41 healthy men during normal daily living (M = 27.9 tests). Bayesian CT analysis revealed a diminishing effect of each hormone on itself as time-interval length or lag increased. In both groups, cortisol had a negative lagged effect on testosterone that persisted for around three days. The cortisol effect on testosterone peaked after 0.71 and 0.51 days in athletic (standardized estimate = -0.13) and healthy men (standardized estimate = -0.11), respectively. Further estimates of non-lagged, contemporaneous correlations revealed positive testosterone and cortisol relationships (athlete r = 0.04, healthy r = 0.46). In summary, complex within-person HPA and HPG interplay emerged in two independent male cohorts. Specifically, a rising cortisol concentration was linked to a fall in testosterone concentration at later time points, but concurrently these hormones tended to rise and fall together. Our results suggest that inhibitory and facilitatory hormonal actions coexist on varying timescales, thereby expanding knowledge of HPG and HPA cross-talk in everyday life.

Monotone Inclusions, Acceleration, and Closed-Loop Control

We propose and analyze a new dynamical system with a closed-loop control law in a Hilbert space [Formula: see text], aiming to shed light on the acceleration phenomenon for monotone inclusion problems, which unifies a broad class of optimization, saddle point, and variational inequality (VI) problems under a single framework. Given an operator [Formula: see text] that is maximal monotone, we propose a closed-loop control system that is governed by the operator [Formula: see text], where a feedback law [Formula: see text] is tuned by the resolution of the algebraic equation [Formula: see text] for some [Formula: see text]. Our first contribution is to prove the existence and uniqueness of a global solution via the Cauchy–Lipschitz theorem. We present a simple Lyapunov function for establishing the weak convergence of trajectories via the Opial lemma and strong convergence results under additional conditions. We then prove a global ergodic convergence rate of [Formula: see text] in terms of a gap function and a global pointwise convergence rate of [Formula: see text] in terms of a residue function. Local linear convergence is established in terms of a distance function under an error bound condition. Further, we provide an algorithmic framework based on the implicit discretization of our system in a Euclidean setting, generalizing the large-step hybrid proximal extragradient framework. Even though the discrete-time analysis is a simplification and generalization of existing analyses for a bounded domain, it is largely motivated by the aforementioned continuous-time analysis, illustrating the fundamental role that the closed-loop control plays in acceleration in monotone inclusion. A highlight of our analysis is a new result concerning [Formula: see text]-order tensor algorithms for monotone inclusion problems, complementing the recent analysis for saddle point and VI problems. Funding: This work was supported in part by the Mathematical Data Science Program of the Office of Naval Research [Grant N00014-18-1-2764] and by the Vannevar Bush Faculty Fellowship Program [Grant N00014-21-1-2941].

Analyzing Longitudinal Multirater Data with Individually Varying Time Intervals

Numerous models have been proposed for the analysis of convergent validity in longitudinal multimethod designs. However, existing multimethod models are limited to measurement designs with equally spaced time intervals. We present a new multirater latent state-trait model with autoregressive effects (MR-LST-AR) for designs with structurally different raters and individually varying time intervals. The new model is illustrated using the German Family Panel pairfam. By means of stochastic differential equations, we show how key coefficients of convergent and discriminant validity can be examined as a function of time. We compare the results from continuous and discrete time analysis and provide code to fit the new model in ctsem. Finally, the advantages and limitations of the model are discussed, and practical recommendations are provided.

Convergence Rates of the Heavy Ball Method for Quasi-strongly Convex Optimization

In this paper, we study the behavior of solutions of the ODE associated to the Heavy Ball method. Since the pioneering work of B.T. Polyak [25], it is well known that such a scheme is very efficient for C2 strongly convex functions with Lipschitz gradient. But much less is known when the C2 assumption is dropped. Depending on the geometry of the function to minimize, we obtain optimal convergence rates for the class of convex functions with some additional regularity such as quasi-strong convexity or strong convexity. We perform this analysis in continuous time for the ODE, and then we transpose these results for discrete optimization schemes. In particular, we propose a variant of the Heavy Ball algorithm which has the best state of the art convergence rate for first order methods to minimize strongly, composite non smooth convex functions.

Continuous-Time Modeling of the Bidirectional Relationship Between Incidental Affect and Physical Activity.

Previous research suggests that there is a bidirectional relationship between incidental affect (i.e., how people feel in day-to-day life) and physical activity behavior. However, many inconsistencies exist in the body of work due to the lag interval between affect and physical activity measurements. Using a novel continuous-time analysis paradigm, we examined the temporal specificity underlying the dynamic relationship between positive and negative incidental affective states and moderate-to-vigorous physical activity (MVPA). A community sample of adults (n = 126, Mage = 27.71, 51.6% Male) completed a 14-day ambulatory assessment protocol measuring momentary positive and negative incidental affect six times a day while wearing a physical activity monitor (Fitbit). Hierarchical Bayesian continuous-time structural equation modeling was used to elucidate the underlying dynamics of the relationship between incidental affective states and MVPA. Based on the continuous-time cross-effects, positive and negative incidental affect predicted subsequent MVPA. Furthermore, engaging in MVPA predicted subsequent positive and negative incidental affect. Incidental affective states had a greater relative influence on predicting subsequent MVPA compared to the reciprocal relationship. Analysis of the discrete-time coefficients suggests that cross-lagged effects increase as the time interval between measurements increase, peaking at about 8 h between measurement occasions before beginning to dissipate. The results provide support for a recursive relationship between incidental affective states and MVPA, which is particularly strong at 7-9 hr time intervals. Future research designs should consider these medium-term dynamics, for both theory development and intervention.

A Note on the Robustness of the Disturbance Observer-Based Robust Control Systems

Abstract This brief shows that the design constraints on the plant-model mismatch and the bandwidth of the disturbance observer (DOb) become more severe when the robust controller is implemented using computers. This brief also shows that continuous-time analysis methods fall-short in explaining the fundamental design constraints of the DOb-based robust digital control systems, therefore leading to unexpected stability and performance problems in practice.

A control-theoretic perspective on optimal high-order optimization

We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function varPhi : {mathbb {R}}^d rightarrow {mathbb {R}} that is convex and twice continuously differentiable, we study a closed-loop control system that is governed by the operators nabla varPhi and nabla ^2 varPhi together with a feedback control law lambda (cdot ) satisfying the algebraic equation (lambda (t))^pVert nabla varPhi (x(t))Vert ^{p-1} = theta for some theta in (0, 1). Our first contribution is to prove the existence and uniqueness of a local solution to this system via the Banach fixed-point theorem. We present a simple yet nontrivial Lyapunov function that allows us to establish the existence and uniqueness of a global solution under certain regularity conditions and analyze the convergence properties of trajectories. The rate of convergence is O(1/t^{(3p+1)/2}) in terms of objective function gap and O(1/t^{3p}) in terms of squared gradient norm. Our second contribution is to provide two algorithmic frameworks obtained from discretization of our continuous-time system, one of which generalizes the large-step A-HPE framework of Monteiro and Svaiter (SIAM J Optim 23(2):1092–1125, 2013) and the other of which leads to a new optimal p-th order tensor algorithm. While our discrete-time analysis can be seen as a simplification and generalization of Monteiro and Svaiter (2013), it is largely motivated by the aforementioned continuous-time analysis, demonstrating the fundamental role that the feedback control plays in optimal acceleration and the clear advantage that the continuous-time perspective brings to algorithmic design. A highlight of our analysis is that we show that all of the p-th order optimal tensor algorithms that we discuss minimize the squared gradient norm at a rate of O(k^{-3p}), which complements the recent analysis in Gasnikov et al. (in: COLT, PMLR, pp 1374–1391, 2019), Jiang et al. (in: COLT, PMLR, pp 1799–1801, 2019) and Bubeck et al. (in: COLT, PMLR, pp 492–507, 2019).

Gated Recurrent Units Viewed Through the Lens of Continuous Time Dynamical Systems.

Gated recurrent units (GRUs) are specialized memory elements for building recurrent neural networks. Despite their incredible success on various tasks, including extracting dynamics underlying neural data, little is understood about the specific dynamics representable in a GRU network. As a result, it is both difficult to know a priori how successful a GRU network will perform on a given task, and also their capacity to mimic the underlying behavior of their biological counterparts. Using a continuous time analysis, we gain intuition on the inner workings of GRU networks. We restrict our presentation to low dimensions, allowing for a comprehensive visualization. We found a surprisingly rich repertoire of dynamical features that includes stable limit cycles (nonlinear oscillations), multi-stable dynamics with various topologies, and homoclinic bifurcations. At the same time we were unable to train GRU networks to produce continuous attractors, which are hypothesized to exist in biological neural networks. We contextualize the usefulness of different kinds of observed dynamics and support our claims experimentally.

Intraindividual dynamics between alliance and symptom severity in long-term psychotherapy: Why time matters.

Objective: The association between alliance and therapy outcome is one of the most investigated factors in psychotherapy research. However, even studies using advanced methods estimate effects over a specific time period (interval) between measurement occasions. Thus, it remains unknown how the magnitude and direction of effects depend on the considered time interval, resulting in limited comparability across studies. The current study examines the influence of time on the within-person relationship between alliance and symptom severity. Method: Alliance (WAI-SR) and symptom severity (SCL-K11) were assessed every fifth session in N = 650 patients receiving up to 100 weekly sessions (mode = 55; M = 41.03; SD = 27.23) of individual psychotherapy in a German outpatient clinic. Bivariate continuous-time (CT) structural equation modeling (SEM) was used to estimate within-person cross- and auto-effects. Results: Analysis revealed significant reciprocal within-person cross-effects with stronger relative effects of SCL-K11 on WAI-SR (a₂₁) than vice versa (a₁₂). CT analysis showed that both cross-lagged effects increased for longer time intervals with strongest effects for time intervals of about 40 sessions (a₂₁ = -.47; a₁₂ = -.19). Conclusions: Alliance and symptom severity showed a reciprocal relationship. Expanding current evidence, our analysis showed how the magnitude of these effects depends on the considered time interval. Applying CT-SEM on longitudinal data of the alliance outcome association complements current cross-lagged panel analysis and allows to compare results of studies which are based on different time intervals between measurement occasions. Methodological, theoretical, and clinical implications are discussed. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Neurofeedback Learning Is Skill Acquisition but Does Not Guarantee Treatment Benefit: Continuous-Time Analysis of Learning-Curves From a Clinical Trial for ADHD

Neurofeedback for attention deficit/hyperactivity disorder (ADHD) has long been studied as an alternative to medication, promising non-invasive treatment with minimal side-effects and sustained outcome. However, debate continues over the efficacy of neurofeedback, partly because existing evidence for efficacy is mixed and often non-specific, with unclear relationships between prognostic variables, patient performance when learning to self-regulate, and treatment outcomes. We report an extensive analysis on the understudied area of neurofeedback learning. Our data comes from a randomised controlled clinical trial in adults with ADHD (registered trial ISRCTN13915109; N = 23; 13:10 female:male; age 25–57). Patients were treated with either theta-beta ratio or sensorimotor-rhythm regimes for 40 one-hour sessions. We classify 11 learners vs 12 non-learners by the significance of random slopes in a linear mixed growth-curve model. We then analyse the predictors, outcomes, and processes of learners vs non-learners, using these groups as mutual controls. Significant predictive relationships were found in anxiety disorder (GAD), dissociative experience (DES), and behavioural inhibition (BIS) scores obtained during screening. Low DES, but high GAD and BIS, predicted positive learning. Patterns of behavioural outcomes from Test Of Variables of Attention, and symptoms from adult ADHD Self-Report Scale, suggested that learning itself is not required for positive outcomes. Finally, the learning process was analysed using structural-equations modelling with continuous-time data, estimating the short-term and sustained impact of each session on learning. A key finding is that our results support the conceptualisation of neurofeedback learning as skill acquisition, and not merely operant conditioning as originally proposed in the literature.

A three-country Kaldorian business cycle model with fixed exchange rates: A continuous time analysis

<p style='text-indent:20px;'>This paper analyses a three-country, fixed exchange rates Kaldorian nonlinear macroeconomic model of business cycles. The countries are connected through international trade, and international capital movement with imperfect capital mobility. Our model is a continuous time version of the discrete time three-country Kaldorian model of Inaba and Asada [<xref ref-type="bibr" rid="b22">22</xref>]. Their paper provided numerical studies of the dynamics of the three countries under fixed exchange rates. This paper provides analytical examinations of the local stability of the model´s equilibria, and of the existence of business cycles. The results are illustrated by numerical simulations.</p>

Understanding temporal aggregation effects on kurtosis in financial indices

Indices of financial returns typically display sample kurtosis that declines towards the Gaussian value 3 as the sampling interval increases. This paper uses stochastic unit root (STUR) and continuous time analysis to explain the phenomenon. Limit theory for the sample kurtosis reveals that STUR specifications provide two sources of excess kurtosis, both of which decline with the sampling interval. Limiting kurtosis is shown to be random and is a functional of the limiting price process. Using a continuous time version of the model under no-drift, local drift, and drift inclusions, we suggest a new continuous time kurtosis measure for financial returns that assists in reconciling these models with the empirical kurtosis characteristics of returns. Simulations are reported and applications to several financial indices demonstrate the usefulness of this approach.