Continuous Time Research Articles

A micro-foundation of a simple financial model with finite-time singularity bubble and its agent-based simulation

This paper proposes a mathematical model of financial security prices in continuous time with bubbles in which prices may diverge and crash in finite time. Just before the bubbles burst, prices increase super-exponentially. In addition, a discrete-time excess demand model is proposed to provide a micro-foundation for the continuous-time model. The derived discrete-time security price model has the same characteristics as the continuous-time price model and expresses the finite-time singularity. Furthermore, based on the excess demand model, an agent-based simulation is performed to check the price behavior. As expected, we can confirm that prices can diverge in finite time and increase super-exponentially.

A generalized model of the Colonel Blotto stochastic game

Abstract A generalized stochastic modification of the Colonel Blotto game, also known as the game of gladiators, is considered. In the original model, each of two players has a set of gladiators with given strengths. The battle of gladiator teams takes place through individual gladiator battles. In each fight, the probability of gladiator winning is proportional to its strength. Kaminsky et al. in 1984 had obtained a formula for the probability of winning in terms of weighted sums of exponential random variables. Here we provide an interpretation of this result from the Markov chains with continuous time point of view, and a more general statement of the problem is considered, for which a similar expression is obtained.

A maximum principle for progressive optimal control of mean‐field forward–backward stochastic system involving random jumps and impulse controls

AbstractIn this paper, we study an optimal control problem of a mean‐field forward–backward stochastic system with random jumps in progressive structure, where both regular and singular controls are considered in our formula. In virtue of the variational technology, the related stochastic maximum principle (SMP) has been obtained, and it is essentially different from that in the classical predictable structure. Specifically, there are three parts in our SMP, that is, continuous part, jump part, and impulse part, and they are, respectively, used to characterize the characteristics of the optimal controls at continuous time, jump time, and impulse time. This shows that the progressive structure can more accurately describe the characteristics of the optimal control at the jump time. We also give two linear–quadratic examples to show the significance of our results.

Experimental study and performance improvement of recycled building bricks based on microwave sintering technology

The preparation of recycled building bricks (RBB) from construction spoil with microwave technology is a green, highly efficient, and energy-saving method. However, the low dielectric loss and high sintering temperature of construction spoil result in a long continuous heating time, which is not conducive to energy conservation or the lifespan of microwave equipment. This study proposes the use of hematite tailings as an auxiliary sintering material to enhance the response of RBB to microwave radiation. Orthogonal experiments were used to analyze the influence of the mass fraction of hematite tailings, the mass fraction fly ash, forming pressure and sintering temperature on the sintering efficiency, mechanical properties, and other basic properties of RBB. The optimum materials and process parameters for manufacturing RBB were obtained. These results indicated that hematite tailings can effectively improve the sintering efficiency of RBB under microwave radiation. The mass fraction of tailings is the most important factor affecting the sintering efficiency, and sintering efficiency increases with an increase in the tailings mass fraction. These four factors have a significant impact on the mechanical properties of RBB. Higher sintering temperature and forming pressure improve the compressive strength, which will decrease with the increasing mass fraction of tailings and fly ash. The average compressive strength of the samples in No. 9 group was the highest, reaching 34.44 MPa. The No. 9 group (30 wt% hematite tailings, 4 wt% fly ash, 66 wt% construction spoil, 20 MPa forming pressure and 800 °C sintering temperature) is considered the best material and process parameter combination for manufacturing RBB with microwave technology due to its highest strength, high solid waste content, good sintering efficiency and performance.

Research on rapid extraction of internal resistance of lithium battery based on short-time transient response

Unlike laboratory measurements and online parameter observations based on long-term continuous operation data, offline fast measurement of battery parameters is widely used for convenient and accurate acquisition of battery parameters in battery production and maintenance processes. However, too short allowable measurement time in engineering results in a small amount of dynamic information that the algorithm can obtain and unclear initial state values, making it difficult to improve the accuracy of the algorithm. This paper employs a local coordinate system established in the vicinity of the measurement moment to extract the transient behavior of battery terminal voltage response under excitation current, and investigates the characterization capability of these transients on ohmic and polarization internal resistance of batteries at different time points. Moreover, based on an equivalent circuit model, it evaluates how initial values of transient voltage affect accuracy in calculating internal resistance. Through customized working condition verification, the selection principles for rapid identification of time points and the basic requirements for excitation conditions have been determined. Comparative verification of online parameter identification results based on continuous time series demonstrates that the fast identification algorithm can accurately identify Ohmic internal resistance and effectively characterize the variation law of battery polarization.

Closed-loop optimisation of neural networks for the design of feedback policies under uncertainty

Solving model predictive control (MPC) problems online can be computationally intractable, especially when considering uncertainty and nonlinear systems. One approach to avoid this is to train a neural network on a data-set of solutions of MPC problems (potentially nonlinear) offline, and to evaluate the trained control policy online. However, due to the separation of these optimisation problems the neural network controller must be carefully verified to ensure adequate closed loop performance. In this paper we propose a method to train a neural network in closed loop for control systems, in continuous or discrete time, while allowing for flexible consideration of parametric uncertainty. This method does not require off-line solutions of the NMPC problem, and instead directly optimises the desired closed loop performance. We prove that our method can approximate the optimal closed-loop control policy to arbitrary tolerance and in numerical examples demonstrate its performance compared to explicit MPC, imitation learning and nominal MPC.

Experimental Study on the Isolation Effect of an Active Flame-Proof Device on a Gas Explosion in an Underground Coal Mine

Passive explosion-isolation facilities in underground coal mines, such as explosion-proof water troughs and bags, face challenges aligned with current trends in intelligent and unmanned technologies, due to restricted applicability and structural features. Grounded in the propagation laws and disaster mechanisms of gas explosions, the device in this paper enables accurate identification of explosion flames and pressure information. Utilizing a high-speed processor for rapid logical processing enables judgments within 1 ms. Graded activation of the operating mechanism is enabled by the device. The tunnel flame-proof device’s flame-extinguishing agent has a continuous action time of 6075 ms. Experiments on the active flame-proof effect of a 100 m3 gas explosion were conducted using a cross-sectional 7.2 m2 large-tunnel test system. With a dosage of 5.6 kg/m2, the powder flame-extinguishing agent completely extinguished the explosion flame within a 20 m range behind the explosion isolator. Numerical calculations unveiled the gas-phase chemical suppression mechanism of the powder flame-extinguishing agent NH4H2PO4 in suppressing methane explosions. Building upon these findings, application technology for active flame-proofing was developed, offering technical support for intelligent prevention and control of gas explosions in underground coal mines.

Recovering Developmental Bivariate Trajectories in Accelerated Longitudinal Designs with Dynamic Continuous Time Modeling

Accelerated longitudinal designs (ALDs) provide an opportunity to capture long developmental periods in a shorter time framework using a relatively small number of assessments. Prior literature has investigated whether univariate developmental processes can be characterized with data obtained from ALDs. However, many important questions in psychology and related sciences imply working with several variables that are intercorrelated as they unfold over time, such as cognitive and cortical development. Therefore, bivariate developmental models are required. This study aimed to assess the effectiveness of continuous-time bivariate Latent Change Score (CT-BLCS) models for recovering the trajectories of two interdependent developmental processes using data from diverse ALDs. Through a Monte Carlo simulation study, the efficacy of different sampling designs and sample sizes was examined. The study fills a gap in the literature by examining the performance of ALDs in bivariate systems, providing specific recommendations for future application of ALDs for studying interrelated developmental variables.

Confidence intervals of survival predictions with neural networks trained on molecular data

In medicine, an important objective is predicting patients’ survival based on their molecular and clinical characteristics. In this context, neural networks have recently been used for their ability to capture complex interactions in the data. Measuring the uncertainty associated with survival estimates obtained by neural networks is essential to enhance predictions’ reliability. We compared four methods adapted to multilayer perceptrons (MLPs) for building confidence intervals at the patient level. The methods were based either on bootstrap with Boot (Efron, 1979), ensembling with DeepEns (Lakshminarayanan et al., 2016), or Monte-Carlo Dropout with MCDrop and BMask (Gal and Ghahramani, 2016; Mancini et al., 2020). A comparison was made through MLP-based survival models: CoxCC and CoxTime (Kvamme et al., 2019) in a continuous time framework, DeepHit (Lee et al., 2018) and PLANN (Biganzoli et al., 1998) in a discrete time framework. We applied the methods to a simulation study, enabling us to estimate a coverage rate of the estimated confidence intervals. We also applied them to real-world datasets, and predicted the survival probability for patients with breast cancer and patients with lung cancer.In the simulation study, CoxCC and CoxTime obtained the mean C-indices numerically closest to those from the Oracle model (mean C-index of 0.723 for CoxCC, 0.726 for CoxTime, versus 0.743 for the Oracle model). Regarding the confidence intervals of survival probabilities, Boot with CoxCC obtained a coverage rate of 96.5%, the closest to the nominal value of 95%. MCDrop was slightly anticonservative and obtained a coverage rate of 89.8% with CoxTime. This method may represent a reasonable compromise in terms of coverage with regards of computational time. In the breast cancer cohort, MLPs had difficulty capturing additional prognostic information from the molecular data. In contrast, in the lung cancer cohort, the models led to substantially stronger discrimination values when adding molecular data to the clinical variables. In conclusion, we were able to represent uncertainty in the survival estimates at particular time points at the patient level using MLPs in the form of 95% confidence intervals. We recommend using CoxTime with either Boot or, for a less intensive computation time, MCDrop.

Characterization of trajectories of physical activity and cigarette smoking from early adolescence to adulthood

BackgroundCigarette smoking and physical inactivity are two critical risk factors for noncommunicable diseases and all-cause mortality. However, few studies have compared the long-term trajectories of both behaviors, as well as multilevel factors associated with trajectory patterns. Using the National Longitudinal Study of Adolescent to Adult Health (Add Health) Wave I through V survey data, this study characterized distinct subgroups of the population sharing similar behavioral patterns from adolescence to adulthood, as well as predictors of subgroup membership for physical activity (PA) and cigarette smoking behavior respectively.MethodsUsing the Add Health Wave I through V survey data, we identified the optimal number of latent classes and class-specific trajectories of PA and cigarette smoking from early adolescence to adulthood, fitting latent growth mixture models with standardized PA score and past 30-day cigarette smoking intensity as outcome measures and age as a continuous time variable. Associations of baseline sociodemographic factors, neighborhood characteristics, and sociopsychological factors with trajectory class membership were assessed using multinomial logistic regression.ResultsWe identified three distinct subgroups of non-linear PA trajectories in the study population: moderately active group (N = 1067, 5%), persistently inactive group (N = 14,257, 69%) and worsening activity group (N = 5410, 26%). Foror cigarette smoking, we identified three distinct non-linear trajectory subgroups: persistent non-smoker (N = 14,939, 72%), gradual quitter (N = 2357, 11%), and progressing smoker (N = 3393, 16%). Sex, race/ethnicity, neighborhood environment and perceived peer support during adolescence were significant predictors of both physical activity and cigarette smoking trajectory subgroup membership from early adolescence to adulthood.ConclusionsThere are three distinct subgroups of individuals sharing similar PA and cigarette smoking behavioral profile respectively from adolescence to adulthood in the Add Health study population. Behavioral interventions that focus on neighborhood environment (e.g. establish community-based activity center) and relationship to peers during adolescence (e.g. peer counseling) could be key to long-term PA promotion and cigarette smoking cessation.

Optimal Proof-Testing Strategies for Safety-Related Systems Based on Continuous Time Markov Chain

Maintenance activities for safety-related systems are generally required to ensure that the systems are working as intended. Regarding the maintenance activities, proof-testing is known as scheduled inspections and maintenance activities for detecting dangerous undetected faults which cannot be detected by diagnostic testing systems installed in the safety-related systems. However, the proof-testing needs a lot of cost and provokes decreasing of the availability for the whole system because the whole system is needed to shut down for proofing that the whole system is working as intended. We discuss analytical methodologies for obtaining optimal proof-testing interval with harmful risk and proof-testing cost by describing the behavior of the safety-related system based on a continuous-time Markov chain. Further, an analytical optimal policy for obtaining economic proof-testing interval is proposed in this paper.

A Review of Birth-Death and Other Markovian Discrete-Time Queues

In this review article, we consider discrete-time birth-death processes and their applications to discrete-time queues. To make the analysis simpler to follow, we focus on transform-free methods and consider instances of non-birth-death Markovian discrete-time systems. We present a number of results within one discrete-time framework that parallels the treatment of continuous time models. This approach has two advantages; first, it unifies the treatment of several discrete-time models in one framework, and second, it parallels to the extent possible the treatment of continuous time models. This allows us to draw parallels and contrasts between the discrete and continuous time queues. Specifically, we focus on birth-death applications to the single server discrete-time model with Bernoulli arrivals and geometric service times and provide the reader with a simple rigorous detailed analysis that covers all five scheduling rules considered in the literature, with attention to stationary distributions at slot edges, slot centers, and prearrival epochs. We also cover the waiting time distributions. Moreover, we cover three Markovian models that fit the global balance equations. Our approach provides interesting insights into the behavior of discrete-time queues. The article is intended for those who are familiar with queueing theory basics and would like a simple, yet rigorous introductory treatment to discrete-time queues.

Thermal bleaching in the northern South China Sea: impact of abnormal environment and climate on high-latitude coral reefs.

Extensive coral bleaching events can result in catastrophic degradation of coral reefs and reorganization of coral communities. In the present study, we analyzed the spatial differences in coral bleaching and possible reasons of large-scale coral bleaching, based on the results of a survey carried out in the northern South China Sea in 2020. In addition, we have continuously monitored the sea surface temperature (SST) of the northernmost Weizhou Island for more than six years. The living coral cover at Weizhou Island (W), Xuwen Nature Reserve (X), and Haihua Island (H) was relatively high at 24.6% ± 4.8%, 12.1% ± 3.8%, and 8.1% ± 2.6%, respectively, whereas their bleaching rates were 9.7% ± 2.6%, 9.7% ± 3.3%, and 6.9% ± 2.1%, respectively. Among them, the living coral cover of W was significantly different from those of X and H, whereas the bleaching rate was not significantly different among the three areas. In all three areas, the massive and encrusting corals predominate and exhibit relatively high bleaching rates, with Porites lutea and Bernardpora stutchburyi being the dominant species. In addition, the temperature monitoring results of Weizhou Island for six consecutive years showed that the critical SST of coral bleaching was 31.5 ℃. The monitoring results also showed that the average SST of Weizhou Island was 32.1 ℃, exceeding 32 ℃ in July 2020 for up to 533h. The longest continuous time when the SST exceeded 32 ℃ was 97h. These findings indicated that the coral bleaching event that occurred in the Beibu Gulf during 2020 was a large-scale and high-temperature transient event that presented a relatively homogeneous threat to the coral communities. We inferred that this sudden heat stress event was caused by the enclosed tidal current in the Beibu Gulf, which prevented the southern upwelling from reaching the north, as well as by the inability of the SST to decrease without rainfall caused by typhoon cyclones. Our findings suggested that abnormal heat waves can result in coral bleaching at high latitudes and even coral reef degradation. Furthermore, our study provides a new perspective for investigating the self-recovery and reorganization of coral communities following accumulated coral bleaching.

Applying a zero-corrected, gravity model estimator reduces bias due to heterogeneity in healthcare utilization in community-scale, passive surveillance datasets of endemic diseases

Data on population health are vital to evidence-based decision making but are rarely adequately localized or updated in continuous time. They also suffer from low ascertainment rates, particularly in rural areas where barriers to healthcare can cause infrequent touch points with the health system. Here, we demonstrate a novel statistical method to estimate the incidence of endemic diseases at the community level from passive surveillance data collected at primary health centers. The zero-corrected, gravity-model (ZERO-G) estimator explicitly models sampling intensity as a function of health facility characteristics and statistically accounts for extremely low rates of ascertainment. The result is a standardized, real-time estimate of disease incidence at a spatial resolution nearly ten times finer than typically reported by facility-based passive surveillance systems. We assessed the robustness of this method by applying it to a case study of field-collected malaria incidence rates from a rural health district in southeastern Madagascar. The ZERO-G estimator decreased geographic and financial bias in the dataset by over 90% and doubled the agreement rate between spatial patterns in malaria incidence and incidence estimates derived from prevalence surveys. The ZERO-G estimator is a promising method for adjusting passive surveillance data of common, endemic diseases, increasing the availability of continuously updated, high quality surveillance datasets at the community scale.

Midyear or End of Year Present Value Factors? Clues from Valuation in Discrete and Continuous Time

This article addresses whether appraisers should be using midyear or end-of-year present value factors. Although this is a topic that other authors and I have addressed, this article has some unique and novel approaches to the topic. The mathematics in this article accounts for cash flow growth within and between years rather than between years only, as others have modeled. We model in both discrete and continuous time, with discrete time in multiple time frames, almost continuous, daily, monthly, quarterly, and annual cash flows. Our continuous time results are very surprising. We conclude that, absent strong seasonality, midyear annual cash flows are very accurate and very little difference is seen in valuation results between quarterly, monthly, daily, and continuous cash flows. They are all close to midyear Gordon model multiple results.

Thermodynamic Formalism for Continuous-Time Quantum Markov Semigroups: the Detailed Balance Condition, Entropy, Pressure and Equilibrium Quantum Processes

Let [Formula: see text] denote the set of [Formula: see text] by [Formula: see text] complex matrices. Consider continuous time quantum semigroups [Formula: see text], [Formula: see text], where [Formula: see text] is the infinitesimal generator. If we assume that [Formula: see text], we will call [Formula: see text], [Formula: see text] a quantum Markov semigroup. Given a stationary density matrix [Formula: see text], for the quantum Markov semigroup [Formula: see text], [Formula: see text], we can define a continuous time stationary quantum Markov process, denoted by [Formula: see text], [Formula: see text] Given an a priori Laplacian operator [Formula: see text], we will present a natural concept of entropy for a class of density matrices on [Formula: see text]. Given a Hermitian operator [Formula: see text] (which plays the role of a Hamiltonian), we will study a version of the variational principle of pressure for [Formula: see text]. A density matrix [Formula: see text] maximizing pressure will be called an equilibrium density matrix. From [Formula: see text] we will derive a new infinitesimal generator [Formula: see text]. Finally, the continuous time quantum Markov process defined by the semigroup [Formula: see text], [Formula: see text], and an initial stationary density matrix, will be called the continuous time equilibrium quantum Markov process for the Hamiltonian [Formula: see text]. It corresponds to the quantum thermodynamical equilibrium for the action of the Hamiltonian [Formula: see text].

Budget deficit and money holding when consumers live forever in an endogenous growth model

<p class="MsoNormal" style="margin-top: 12pt; text-align: justify;"><span lang="EN-US" style="font-family: arial, helvetica, sans-serif;">In this paper I will show that budget deficit (or fiscal deficit) is necessary to achieve full employment under constant prices or inflation, using a model of endogenous growth in which consumers hold money for the reason of liquidity and live forever. Budget deficit need not be offset by future budget surpluses. I consider the continuous time case by taking the limit of the discrete time case when the time interval approaches zero. A continuous time dynamic model seems to be more general than a discrete time model. When the actual budget deficit is greater (smaller) than the value which is necessary and sufficient for full employment under constant prices, an inflation (a recession) occurs. The main argument of this paper is that a growing economy requires the continuation of budget deficit, and that we should not think of paying off the resulting government debt with taxes.</span></p>

Regularized continuous time structural equation models: A network perspective.

Regularized continuous time structural equation models are proposed to address two recent challenges in longitudinal research: Unequally spaced measurement occasions and high model complexity. Unequally spaced measurement occasions are part of most longitudinal studies, sometimes intentionally (e.g., in experience sampling methods) sometimes unintentionally (e.g., due to missing data). Yet, prominent dynamic models, such as the autoregressive cross-lagged model, assume equally spaced measurement occasions. If this assumption is violated parameter estimates can be biased, potentially leading to false conclusions. Continuous time structural equation models (CTSEM) resolve this problem by taking the exact time point of a measurement into account. This allows for any arbitrary measurement scheme. We combine CTSEM with LASSO and adaptive LASSO regularization. Such regularization techniques are especially promising for the increasingly complex models in psychological research, the most prominent example being network models with often dozens or hundreds of parameters. Here, LASSO regularization can reduce the risk of overfitting and simplify the model interpretation. In this article we highlight unique challenges in regularizing continuous time dynamic models, such as standardization or the optimization of the objective function, and offer different solutions. Our approach is implemented in the R (R Core Team, 2022) package regCtsem. We demonstrate the use of regCtsem in a simulation study, showing that the proposed regularization improves the parameter estimates, especially in small samples. The approach correctly eliminates true-zero parameters while retaining true-nonzero parameters. We present two empirical examples and end with a discussion on current limitations and future research directions. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Collective signalling drives rapid jumping between cell states.

Development can proceed in 'fits and starts', with rapid transitions between cell states involving concerted transcriptome-wide changes in gene expression. However, it is not clear how these transitions are regulated in complex cell populations, in which cells receive multiple inputs. We address this issue using Dictyostelium cells undergoing development in their physiological niche. A continuous single cell transcriptomics time series identifies a sharp 'jump' in global gene expression marking functionally different cell states. By simultaneously imaging the physiological dynamics of transcription and signalling, we show the jump coincides with the onset of collective oscillations of cAMP. Optogenetic control of cAMP pulses shows that different jump genes respond to distinct dynamic features of signalling. Late jump gene expression changes are almost completely dependent on cAMP, whereas transcript changes at the onset of the jump require additional input. The coupling of collective signalling with gene expression is a potentially powerful strategy to drive robust cell state transitions in heterogeneous signalling environments. Based on the context of the jump, we also conclude that sharp gene expression transitions may not be sufficient for commitment.

Assessing Statistical Indices for Calibrating Building Performance Simulation Models via Continuous Time Series

In engineering planning practice, building simulation is becoming increasingly crucial for evaluating buildings’ energetic and thermal behaviour. The appropriate application in the form of models that represent reality precisely, therefore, faces the challenge of realistic parameter specification for uncertain BES model properties. Many of them can only be restricted to a probable range of values. Additional knowledge can be obtained for the case of available measurement data via inverse modelling. This approach minimises cost function values representing discrepancies between associated time series (measured and simulated data sets). Much research has been published in this field for energy consumption characteristics. These approaches differ in several aspects from measured continuous physical state quantities. This article applies general cost indices to air temperature measurement series. For isolated effects such as time delay and amplitude attenuation, the impact on the characteristic values is examined, and their response is evaluated. This survey leads to the conclusion that there is no single parameter suitable for identifying all effects, and a combination is recommended. A new proposal is made for such a combined statistical index, and exemplary applied for measured temperature curves from a castle near Potsdam.