Finite Time Span Research Articles

Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks.

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási-Albert (BA), Erdös-Rényi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0 with and without mortality, respectively, and prove that RM<R0. For RM,R0>1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.

Output information-based intermittent optimal control for continuous-time nonlinear systems with unmatched uncertainties via adaptive dynamic programming

Intermittent control stands as a valuable strategy for resource conservation and cost reduction across diverse systems. Nonetheless, prevailing research is intractable to address the challenges posed by robust optimal intermittent control of nonlinear input-affine systems with unmatched uncertainties. This paper aims to fill this gap. Initially, we introduce an enhanced finite-time intermittent control approach to ensure stability within nonlinear dynamic systems harboring bounded errors. A neural networks (NNs) state observer is constructed to estimate system information. Subsequently, an optimal intermittent controller that operates within a finite time span, guaranteeing system stability by employing the Hamilton–Jacobi–Bellman (HJB) methodology. Furthermore, we devise an output information-based event-triggered intermittent (ETI) approach rooted in the robust adaptive dynamic programming (ADP) algorithm, furnishing an optimal intermittent control law. In this process, a critic NNs is introduced to estimate the cost function and optimal intermittent controller. Simulation results show that our proposed method is superior to existing intermittent control strategies.

A Vision Dynamics Learning Approach to Robotic Navigation in Unstructured Environments

Autonomous legged navigation in unstructured environments is still an open problem which requires the ability of an intelligent agent to detect and react to potential obstacles found in its area. These obstacles may range from vehicles, pedestrians, or immovable objects in a structured environment, like in highway or city navigation, to unpredictable static and dynamic obstacles in the case of navigating in an unstructured environment, such as a forest road. The latter scenario is usually more difficult to handle, due to the higher unpredictability. In this paper, we propose a vision dynamics approach to the path planning and navigation problem for a quadruped robot, which navigates in an unstructured environment, more specifically on a forest road. Our vision dynamics approach is based on a recurrent neural network that uses an RGB-D sensor as its source of data, constructing sequences of previous depth sensor observations and predicting future observations over a finite time span. We compare our approach with other state-of-the-art methods in obstacle-driven path planning algorithms and perform ablation studies to analyze the impact of architectural changes to our model components, demonstrating that our approach achieves superior performance in terms of successfully generating collision-free trajectories for the intelligent agent.

An optimal maintenance strategy for machining system considering production rates

In this paper, a maintenance strategy is developed to determine the optimal number of preventive maintenance actions to carry out over the finite operating time span H for a manufacturing system satisfying several demands. The system is composed of dry machining which produces two types of products (steel products and aluminum products). At any given time, the machine is able to produce one type of product, and then switches to another. This is done by modeling and minimizing the expected total maintenance cost considering the influence of production rates on the system degradation. A numerical example is presented to illustrate the use of the proposed approach and to discuss the obtained results.

Obsolescence effects in second language phonological networks.

Phonological networks are representations of word forms and their phonological relationships with other words in a given language lexicon. A principle underlying the growth (or evolution) of those networks is preferential attachment, or the "rich-gets-richer" mechanisms, according to which words with many phonological neighbors (or links) are the main beneficiaries of future growth opportunities. Due to their limited number of words, language lexica constitute node-constrained networks where growth cannot keep increasing in a linear way; hence, preferential attachment is likely mitigated by certain factors. The present study investigated obsolescence effects (i.e., a word's finite timespan of being active in terms of growth) in an evolving phonological network of English as a second language. It was found that phonological neighborhoods are constructed by one large initial lexical spurt, followed by sublinear growth spurts that eventually lead to very limited growth in later lexical spurts during network evolution. First-language-given neighborhood densities are rarely reached even by the most advanced language learners. An analysis of the strength of phonological relationships between phonological word forms revealed a tendency to incorporate phonetically more distant phonological neighbors at earlier acquisition stages. Overall, the findings suggest an obsolescence effect in growth that favors younger words. Implications for the second-language lexicon include leveraged learning mechanisms and learning bouts focused on a smaller range of phonological segments, and involve questions concerning lexical processing in aging networks.

Analytical representation for the numerical ephemeris of Titan within short time spans

Context. Numerical integration ephemerides are widely used in research and engineering for their high precision. However, subject to their finite available time spans, their use is limited in theoretical research, such as the studies of rotation and evolution. Previously, we successfully experimented on the analytical representation of the mean longitude of Titan of the Jet Propulsion Laboratory (JPL) ephemeris, as a function of combinations of proper frequencies, and related the results with what is given in the synthetic ephemerides obtained by the Théorie Analytique des Satellites de Saturne (TASS). Aims. In this study, the analytical representations of the other osculating elements of the JPL Titan ephemeris are accomplished in order to construct the new synthetic representations, which have the advantages of both systems: long-lasting stability, the system details of TASS, and the high precision of JPL. Methods. A frequency analysis process was used to obtain the proper frequencies, amplitudes, and phases of the two ephemerides in the short term and the semi-long terms. For the proper frequency of the ascending node of Titan, which has a very long period, it is challenging to acquire the exact value, and the formula of TASS was used. The amplitude and phase of long terms were further calculated by a least-squares procedure. Results. Thanks to the accomplishments of the new synthetic representations of the JPL ephemeris, we report the complete combinations of the osculating elements of Titan. These combinations contain important dynamical information such as the proper frequencies. They will be useful in the theoretical research.

Integrated production-maintenance strategy considering quality constraints in dry machining

ABSTRACT The selection of the suitable production parameters for dry machining remains a challenging task which impacts the productivity, the system degradation and the quality of the output product. This study proposes an integrated production-maintenance policy allowing the simultaneous consideration of the production parameters, mainly the cutting speed, the production time and cost, the preventive maintenance period and the quality levels and the selling prices of the output product. A special feature of this strategy, defined on a finite time span, is to allow a change of the cutting speed at a certain instant to be determined in an optimal way concurrently with the preventive maintenance period, such as to maximise the total expected profit per time unit. A mathematical model is developed to express the average profit per time unit as a function of the decision variables. A solving procedure is also proposed. A numerical example and a sensitivity analysis are presented in order to show the impact of some major input parameters on the optimal policy.

Analysis of a stage-dependent epidemic model based on a non-Markov random process

We present some stochastic model of an infection spread among the adult population of a certain region. The model bases on a random birth and death process supplemented by the point distributions that reflect the durations of stay of individuals at various stages of the disease. The durations of some stages of the disease are assumed constant. The model is a stochastic analog of a system of delay differential equations and convolution integral equations describing the infection spread in the deterministic approach. We address the problem of the infection eradication over a time span comparable to the average lifetime of several generations of individuals. The results of computational experiments are presented, where the dynamics of mathematical expectations of the size of certain groups of individuals is studied and the probability of the infection eradication over a finite time span is estimated using the Monte Carlo method.

REAL OPTION SIGNALING GAMES OF DEBT FINANCING USING EQUITY GUARANTEE SWAPS UNDER ASYMMETRIC INFORMATION

We analyze the real option signaling game models of debt financing of a risky project under information asymmetry, where the firm quality is only known to the firm management but not outsiders. The firm decides on the optimal investment timing of the risky project that requires upfront fixed funding cost and subsequent operating costs. The fixed funding cost is financed via either direct bank loan or entering into a three-party equity guarantee swap (EGS) that involves a bank granting the loan and third party guarantor. Under the EGS agreement, the guarantor is obligated to pay all the future coupon stream to the bank upon default of the firm. In return for the provision of the guarantee, the guarantor obtains certain proportional share of equity of the firm at the time when the swap agreement is signed. The share of equity demanded by the guarantor depends on the outside investors’ belief on the firm quality. The low-type firm has the incentive to mimic the investment strategy of being high-type in terms of investment timing and share of equity. The high-type firm may adopt the appropriate separating strategy by speeding up investment or choosing an alternative financing choice. The resulting loss of the real option value of the investment opportunity represents the information cost under separating strategies. We examine the incentive compatibility constraints faced by the firm under different quality types and discuss characterization of the separating and pooling equilibriums. Unlike the usual assumption of perpetuity of investment opportunity, our real option model assumes the time window of the investment opportunity to be finite. We explore how the information cost and nature of separating and pooling equilibriums evolves over the finite time span of the investment opportunity. The information costs and investment thresholds exhibit interesting time-dependent behaviors. We examine the firm’s investment and financing choice between EGS and the direct bank loan against time and other parameters via comparison of the corresponding information costs and investment thresholds.

Variance reduction approach for the volatility over a finite-time horizon

The volatility is a measure for the uncertainty of an asset’s return and is used to reflect the risk level of a financial asset. In this article, we consider the double kernel nonparametric estimator for the volatility function in a diffusion model over a finite-time span based on high frequency sampling data. Under the minimum conditions, the asymptotic mixed normality for the underlying estimator is derived. Moreover, the better finite-sample performance as variance reduction and even mean squared error reduction of the proposed estimator is verified through a Monte Carlo simulation study and an empirical analysis on overnight Shibor in China.

An Optimal Preventive Maintenance Policy for a Solar Photovoltaic System

In this paper, we develop a preventive maintenance (PM) strategy for a solar photovoltaic system composed of solar panels functioning as a series system. The photovoltaic system is considered in a failed state whenever its efficiency drops below a predefined threshold or any electrical wiring element is damaged. In such a situation of failure, a minimal repair is performed. The proposed PM strategy suggests systematically replacing n panels with their respective wiring system every time units T over a finite operating time span H. The panels to be preventively replaced are selected by the maintenance agent after an on-site overall assessment of all panels, making sure every time not to replace panels previously replaced during a given replacement cycle of all panels of the system. An analytical model is proposed in order to simultaneously determine the optimal PM period, T, and the optimal number of solar panels, n, to be replaced at each PM. This is done by modeling and minimizing the expected total maintenance cost over the finite operating time horizon H. A numerical example is presented to illustrate the use of the proposed modelling approach and to discuss the obtained results. The latter provide the optimal solutions (T*, n*) for different combinations of input parameters. They also show the economic relevance of the proposed PM strategy through estimation of the economic gain when comparing the situations with and without preventive maintenance.

Finite-time event-triggered non-fragile state estimation for discrete-time delayed neural networks with randomly occurring sensor nonlinearity and energy constraints

In this paper, the problem of event-triggered non-fragile state estimator design for discrete-time delayed neural networks (DNNs) is investigated over finite-time span. In consideration of the changes of environment and high sensitivity, external disturbances and/or parameter uncertainties might be involved in estimator parameters of the concerned DNNs. Therefore, it is one of our main objectives to design a non-fragile state estimator subject to the norm bounded gain variation. The sensor nonlinearity is supposed to occur in a random way. In the meanwhile, the event-triggered scheme and energy constraints are adopted in state estimator design for the purpose of energy and resource saving. By using the Lyapunov stability theory and some analytical techniques, sufficient conditions are established to guarantee that the estimation error system is finite-time bounded and meet a prescribed mixed H∞ and passivity performance constraint. Furthermore, the estimator gains are obtained via solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are exploited to demonstrate the effectiveness of the developed technique.

On time scales and quasi-stationary distributions for multitype birth-and-death processes

We consider a class of birth-and-death processes describing a population made of $d$ sub-populations of different types which interact with one another. The state space is $\mathbb{Z}_+^d$ (unbounded). We assume that the population goes almost surely to extinction, so that the unique stationary distribution is the Dirac measure at the origin. These processes are parametrized by a scaling parameter $K$ which can be thought as the order of magnitude of the total size of the population at time $0$. For any fixed finite time span, it is well-known that such processes, when renormalized by $K$, are close, in the limit $K\to+\infty$, to the solutions of a certain differential equation in $\mathbb{R}_+^d$ whose vector field is determined by the birth and death rates. We consider the case where there is a unique attractive fixed point (off the boundary of the positive orthant) for the vector field (while the origin is repulsive). What is expected is that, for $K$ large, the process will stay in the vicinity of the fixed point for a very long time before being absorbed at the origin. To precisely describe this behavior, we prove the existence of a quasi-stationary distribution (qsd). In fact, we establish a bound for the total variation distance between the process conditioned to non-extinction before time $t$ and the qsd. This bound is exponentially small in $t$, for $t\gg \log K$. As a by-product, we obtain an estimate for the mean time to extinction in the qsd. We also quantify how close is the law of the process (not conditioned to non-extinction) either to the Dirac measure at the origin or to the qsd, for times much larger than $\log K$ and much smaller than the mean time to extinction, which is exponentially large as a function of $K$. Let us stress that we are interested in what happens for finite $K$. We obtain results much beyond what large deviation techniques could provide.

Resonance phenomena in option pricing with arbitrage

In this paper, we want to report an interesting resonance phenomena that appears in option pricing, when the presence of arbitrage is incorporated explicitly into the Black–Scholes model. In Contreras et al. (2010), the authors after analyse empirical financial data, determines that the mispricing between the empirical and the Black–Scholes prices can be described by Heaviside type function (called an arbitrage bubble there). These bubbles are characterised by a finite time span and an amplitude which measures the price deviation from the Black–Scholes model. After that, in Contreras et al. (2010), the Black–Scholes equation is generalised to incorporates explicitly these arbitrage bubbles, which generates an interaction potential that changes the usual Black–Scholes free dynamics completely. However, an interesting phenomena appears when the amplitude of the arbitrage bubble is equal to the volatility parameter of the Black–Scholes model: in that case, the potential becomes infinite, and option pricing decrease abruptly to zero. We analyse this limit behaviour for two situations: a European and a barrier option. Also, we perform an analytic study of the propagator in each case, to understand the cause of the resonance. We think that it resonance phenomena could to help to understand the origin of certain financial crisis in the option pricing area.

Real Option Signaling Games of Debt Financing Using Equity Guarantee Swaps under Asymmetric Information

We analyze the real option signaling game models of debt financing of a risky project under information asymmetry, where the firm quality is only known to the firm management but not outsiders. The firm decides on the optimal investment timing of the risky project that requires upfront fixed funding cost and subsequent operating costs. The fixed funding cost is financed via either direct bank loan or entering into a three-party equity guarantee swap (EGS) that involves a bank granting the loan and third party guarantor. Under the EGS agreement, the guarantor is obligated to pay all the future coupon stream to the bank upon default of the firm. In return for the provision of the guarantee, the guarantor obtains certain proportional share of equity of the firm at the time when the swap agreement is signed. The share of equity demanded by the guarantor depends on the outside investors' belief on the firm quality. The low-type firm has the incentive to mimic the investment strategy of being high-type in terms of investment timing and share of equity. The high-type firm may adopt the appropriate separating strategy by speeding up investment or choosing an alternative financing choice. The resulting loss of the real option value of the investment opportunity represents the information cost under separating strategies. We examine the incentive compatibility constraints faced by the firm under different quality types and discuss characterization of the separating and pooling equilibriums. Unlike the usual assumption of perpetuity of investment opportunity, our real option model assumes the time window of the investment opportunity to be finite. We explore how the information cost and nature of separating and pooling equilibriums evolves over the finite time span of the investment opportunity. The information costs and investment thresholds exhibit interesting time dependent behaviors. We examine the firm's investment and financing choice between EGS and the direct bank loan against time and other parameters via comparison of the corresponding information costs and investment thresholds.

Condition-based scheduled maintenance optimization of structures based on reliability requirements under continuous degradation and random shocks

In this paper, a condition-based scheduled maintenance model with aperiodic inspections of structures is developed. The structures are experiencing both a gradual degradation process and a random shock process. The former is characterized by a stationary gamma process (SGP), and the latter is assumed to be a homogeneous Poisson process (HPP). Two typical common failure modes are considered in the reliability and the condition-based maintenance model, namely: (1) soft failures caused by the continuous degradation process, together with sudden damage increments due to shocks with moderate impacts, and (2) hard failures caused by the same shock process when a severe shock occurs. A remaining useful lifetime-based (RUL-based) inspection policy is utilized to determine the inspection schedule. Thereafter, at each inspection point, different maintenance actions are to be determined to minimize the average cost rate for either an infinite or a finite time span. The developed models are demonstrated by a numerical example. Sensitivity analyses of the optimal solution with various model parameters are also performed. It is illustrated that, as compared with the pure continuous degradation process, the additional shock loads exert notable impacts on the optimal maintenance strategies.

Fixed and Long Time Span Jump Tests: New Monte Carlo and Empirical Evidence

Numerous tests designed to detect realized jumps over a fixed time span have been proposed and extensively studied in the financial econometrics literature. These tests differ from “long time span tests” that detect jumps by examining the magnitude of the jump intensity parameter in the data generating process, and which are consistent. In this paper, long span jump tests are compared and contrasted with a variety of fixed span jump tests in a series of Monte Carlo experiments. It is found that both the long time span tests of Corradi et al. (2018) and the fixed span tests of Aït-Sahalia and Jacod (2009) exhibit reasonably good finite sample properties, for time spans both short and long. Various other tests suffer from finite sample distortions, both under sequential testing and under long time spans. The latter finding is new, and confirms the “pitfall” discussed in Huang and Tauchen (2005), of using asymptotic approximations associated with finite time span tests in order to study long time spans of data. An empirical analysis is carried out to investigate the implications of these findings, and “time-span robust” tests indicate that the prevalence of jumps is not as universal as might be expected.

Anomalous Behavior of the Terrestrial Electric Field Intensity at Multiple Frequencies of Relativistic Binary Star Systems

The vertical component of the terrestrial electric field intensity has been proven to be spectrally localized at multiple frequencies of forty-three relativistic binary star systems. The used four time series contain multiannual observations of the terrestrial electric field intensity in the infralow frequency range. The used method is eigenoscopy developed by the present authors. The matrix of second sample moments is computed at finite time spans. The eigenvectors of the moment matrix and their amplitude spectra are computed and analyzed. A database of the discovered anomalous behavior has been built.

Battery and supercapacitor imperfections modeling and comparison for RF energy harvesting wireless sensor network

In an energy harvesting communication system, the main challenge is to improve network lifetime and maximize throughput by allocating optimal power over a finite span of time, with varying channel and energy. Considering (1) causal state information (SI) of channel and energy (CSI and ESI) and (2) energy storage device imperfections, the problem of power allocation is solved using dynamic programming. As compared to the battery, the supercapacitor is a good alternative for network lifetime improvement, but the imperfections hinder the performance. In this paper, imperfections (storage inefficiency and energy leakage equation) are modeled for supercapacitor and battery. We consider a constant leakage rate for battery. Also, the imperfections of battery and supercapacitor are compared to find which imperfection of supercapacitor is a bottleneck in system performance in different settings (varying channel conditions). The analysis is supported by numerical results.

Fixed and Long Time Span Jump Tests: New Monte Carlo and Empirical Evidence

Numerous tests designed to detect realized jumps over a fixed time span have been proposed and extensively studied in the financial econometrics literature. These tests differ from “long time span tests” that detect jumps by examining the magnitude of the intensity parameter in the data generating process, and which are consistent. In this paper, long span tests, including the tests of Corradi et al. (2018) (called CSS tests), are compared and contrasted with a variety of fixed span tests, including the ASJ test of A¨it-Sahalia and Jacod (2009), the BNS test of Barndorff-Nielsen and Shephard (2006), and the PZ test of Podolskij and Ziggel (2010), in an extensive series of Monte Carlo experiments. The long span tests that we examine are consistent against the null hypothesis of zero jump intensity, while the fixed span tests are not designed to detect jumps in the data generating process, and instead detect realized jumps over a fixed time span. It is found that both the ASJ and CSS tests exhibit reasonably good finite sample properties, for time spans both short and long. The other tests suffer from finite sample distortions, both under sequential testing (as is well known) and under long time spans. The latter finding is new, and confirms the “pitfall” discussed in Huang and Tauchen (2005), of using asymptotic approximations associated with finite time span tests in order to study long time spans of data. An extensive empirical analysis is carried out to investigate the implications of these findings. In particular, when applied to stock price and stock index data, “time-span robust” tests indicate that the prevalence of jumps is not as universal as might be expected. Various sector ETFs and individual stocks, for example, appear to exhibit no jumping behavior during a number of quarterly and annual periods.