Linear and Competitive Strategies for Continuous Robot Formation Problems

Many important factors affect the spread of childhood infectious disease. To better understand the fundamental drivers of infectious disease spread, several researchers have estimated seasonal transmission coefficients in discrete-time models. In this paper, we build upon this previous work and also develop a framework for efficient estimation using continuous differential equation models. We introduce nonlinear programming formulations to efficiently estimate model parameters and seasonal transmission profiles from existing case count data for the childhood disease, measles. We compare results from discrete time and continuous time models and address several shortcomings of the discrete-time method, including removing the need for the data reporting interval to match the time between successive cases in the chain of transmission or serial interval of the disease. Using a simultaneous approach for optimization of differential equation systems, we demonstrate that seasonal transmission parameters can be effectively estimated using continuous time models instead of discrete-time models.

American Option Pricing with Discrete and Continuous Time Models: An Empirical Comparison

Limitations record on a variable which have continuous variable changes make the 'time' attached to the data is discrete. That underlies development of continuous time model. Compared to discrete time model, the continuous time model has advantages that can make prediction at different lag. In addition, it still can perform continuous time model parameter estimation, although the objects observations do not always have the same time interval (irregular time). Thus, the purpose of this study is to examine the consistency of continuous time model coefficient parameter with structural equation model (SEM) approach in irregular time data. The method used is the Exact Discrete Model (EDM) with SEM approach. EDM is a model that connects the parameter to value which is underlying parameter of the continuous time model with non-linear relationships. The result analysis of the research indicated that the coefficients of continuous time model parameter are still consistent until 20% of irregular time with 5% consistency limits.

This paper summarizes models for software reliability demonstration testing (SRDT). The models are briefly classified into three types: (1) continuous models, (2) discrete models and (3) models considering damage sizes of software failures. Under the continuous models, the software product of interest is tested for time t and is accepted if the number of software failures in the test does not exceed a prespecified integer s. The values of design variables, t and s are determined based on (i) the concept of a statistical test (a statistical model) and (ii) the Kullback–Leibler information (a K–L model). The K–L model has less parameters to be prespecified than the statistical model. Under the discrete models for SRDT, the software of interest is tested with n input data sets and is accepted if the number of input data sets causing software failures in the test does not exceed a prespecified integer c. A statistical model as well as a K–L model is described for the discrete models. Neither continuous nor discrete models in the above take the damage size of software failures into consideration. The third type of models are continuous and discrete models which consider the cumulative damage size caused by software failures as well as the number of software failures in the test.

New distribution theory for the estimation of structural break point in mean

This article focuses on production planning in the metallurgical sector. This study undertakes a detailed comparative study of mixed-integer linear programming models using different time representations: continuous and discrete. The analysis shows that the continuous model consistently outperforms its discrete counterpart in all evaluated scenarios. The key difference between the continuous and discrete models is the continuous model’s ability to deliver better makespan results, achieving an improvement of up to 15% compared to the discrete model. This advantage holds even in complex environments with a high number of tasks and machines, where the continuous model consistently outperforms the discrete model by over 6% in the scenario with the highest number of tasks and machines. This preference extends beyond makespan considerations. The continuous model also maintains an edge in terms of runtime efficiency, achieving better times with a 99% improvement over the discrete model in all scenarios except one. These findings provide concrete evidence for the use of continuous models, which promise more effective production planning in analogous manufacturing domains.

Number of software Reliability growth models has been proposed in the literature. A mathematical technique which describes the software testing phenomenon known as the software reliability growth model. Software reliability growth models are used to predict the number of faults and reliability of the software. In the view of this software reliability growth models are basically differentiated as the continuous and discrete models. There is a plenty of development in the continuous models but little towards the discrete models. In this paper we have presented a discrete reliability growth model with different discrete testing effort functions and the same time software release policy is discussed. A new imperfect debugging discrete software reliability growth model with testing effort is proposed. All calculations are done on real data. The results shows the proposed testing effort models are perfectly fit to the data.

Benhabib, Schmitt-Grohe, and Uribe (2003) argue that if you relied solely on local analysis you would be led to believe that aggressive, backward-looking interest rate rules are sufficient for determinacy. But from the perspective of global analysis, backward-looking rules do not guarantee uniqueness of equilibrium and indeed may lead to cyclic and even chaotic equilibria. This comment argues that this result is premature. We utilize a discrete time model and make two observations. First, compared to their continuous time model, the cyclic equilibria under a backward-looking rule are much less likely to arise in a discrete time model. Second, pure backward-looking rules are less likely to suffer from these global indeterminacy problems than rules that also include current or future inflation.

R. Garcia-Millan etal. [Phys. Rev. E 91, 042122 (2015)PLEEE81539-375510.1103/PhysRevE.91.042122] reported a universal finite-size scaling form of the survival probability in discrete time branching processes. In this comment, we generalize the argument to a wide range of continuous time branching processes. Owing to the continuity, the resulting differential (rather than difference) equations can be solved in closed form, rendering some approximations by R. Garcia-Millan etal. superfluous, although we work along similar lines. In the case of binary branching, our results are in fact exact. Demonstrating that discrete time and continuous time models have their leading order asymptotics in common, raises the question to what extent corrections are identical.

An interesting class of planning domains, including planning for daily activities of Mars rovers, involves achievement of goals with time constraints and concurrent actions with probabilistic durations. Current probabilistic approaches, which rely on a discrete time model, introduce a blow up in the search state-space when the two factors of action concurrency and action duration uncertainty are combined. Simulation-based and sampling probabilistic planning approaches would cope with this state explosion by avoiding storing all the explored states in memory, but they remain approximate solution approaches. In this paper, we present an alternative approach relying on a continuous time model which avoids the state explosion caused by time stamping in the presence of action concurrency and action duration uncertainty. Time is represented as a continuous random variable. The dependency between state time variables is conveyed by a Bayesian network, which is dynamically generated by a state-based forward-chaining search based on the action descriptions. A generated plan is characterized by a probability of satisfying a goal. The evaluation of this probability is done by making a query the Bayesian network.

Co-operation of electricity and natural gas systems including electric vehicles and variable renewable energy sources based on a continuous-time model approach

COSMOS is a new simulation language for description of continuous, discrete or combined continuous/discrete models. For continuous models, the COSMOS language definition constitutes a superset of CSSL with many additional structuring elements being incorporated, e.g. for convenient modelling of piecewise continuous models and variable structure systems. Discrete models are coded according to the process interaction world view. The design of the language constructs makes it possible to write simulation programs in accordance with modem software engineering methodology. The model and experiment description, for example, are totally separated. In addition, models can be separated into submodels.

Random Cantor set models for the elastic-perfectly plastic contact of rough surfaces

In modern financial economics continuous time-series diffusion models are more convenient to deal with than discrete time models when they are used to depict important economic variables such as stock prices, exchange rates and interest rates. A two-stage estimation approach is proposed to deal with the continuous-time models with jumps, in which the initial settings are quite resilient. This paper presents an example: first, the realized volatility theory is applied to the jumps and diffusion parameters of the model; then it uses forward Kolmogorov equation of actual price distribution at steady state to estimate the drift parameters. The model relies little on initial settings and optimization algorithms. The empirical results show that the estimations are stable and reliable. Hence the model is easier to extend to the estimation of complex set continuous time series.

This paper proposes a new method to stabilize the continuous-time TS fuzzy models by using results from their discretized models. The proposed approach is structured as follows: first, a discrete model is obtained from the discretization of the continuous TS fuzzy model. Second the gains of a non-PDC controller ensuring the stabilization of the discrete model are determined. Third, we check if the discrete control law used continuously without any zero-order hold can stabilize the continuous TS model. It is obvious that two sets of LMIS conditions are obtained: one for the discrete model, and one for the continuous on. But these two sets of LMIS conditions are much easier to solve than a single set of BMIS conditions usually found when a non PDC control law is directly applied to a continuous model. Simulation examples illustrate the effectiveness of this approach.