An algorithmic approach to entanglement-assisted quantum error-correcting codes from the Hermitian curve

<p style='text-indent:20px;'>We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is <inline-formula><tex-math id="M1">\begin{document}$ c $\end{document}</tex-math></inline-formula>, the number of required maximally entangled quantum states since the Hermitian dual of an AG code is unknown. In this article, we present an efficient algorithmic approach for computing <inline-formula><tex-math id="M2">\begin{document}$ c $\end{document}</tex-math></inline-formula> for this family of EAQECCs. As a result, this algorithm allows us to provide EAQECCs with excellent parameters over any field size.</p>

Local Asymptotic Normality Complexity Arising in a Parametric Statistical Lévy Model

We consider statistical experiments associated with a Lévy process X = X t t ≥ 0 observed along a deterministic scheme i u n , 1 ≤ i ≤ n . We assume that under a probability ℙ θ , the r.v. X t , t > 0 , has a probability density function > o , which is regular enough relative to a parameter θ ∈ 0 , ∞ . We prove that the sequence of the associated statistical models has the LAN property at each θ , and we investigate the case when X is the product of an unknown parameter θ by another Lévy process Y with known characteristics. We illustrate the last results by the case where Y is attracted by a stable process.

Analytical solution of the problem of dynamic synthesis of a six-link straight-line converting mechanism of the sucker-rod pumping drive

The paper presents an analytical solution to the problem of optimal dynamic balancing of the six-link converting mechanism of the sucker-rod pumping unit. This problem is solved numerically using a computer model of dynamics, namely by selecting the value of the correction factor k. Here we will consider an analytical method for solving this problem, that is, we find the location of the counterweight on the third link of the six-link converting mechanism for balancing. To solve the problem, we use the principle of possible displacement and write an equation where we express the torque through the unknown parameter of the counterweight. Further, such a value of the unknown parameter is found, at which the minimum of the root-mean-square value of torque M is reached. From the condition of the minimum of the function, we obtain an equation for determining the location of the counterweight. Thus, we obtain an analytical solution to the problem of optimal dynamic balancing of the six-link converting mechanism of the sucker-rod pumping drive in various settings. According to the results, it was found that with the combined balancing method, the value of the maximum torque M and the value of the maximum power are reduced by 20 % than when the counterweight is placed on the third link of the converting mechanism, as well as when the value of the maximum torque is determined through the correction factor k. In practice, balancing is carried out empirically by comparing two peaks of torque M on the crank shaft per cycle of the mechanism movement. Solving the analytical problem, we determine the exact location of the counterweight.

One Parameter A (α) Distribution: Different Methods of Estimation

This paper addresses the different methods of estimation of the unknown parameter of one parameter A(α) distribution from the frequentist point of view. We briefly describe different approaches, namely, maximum likelihood estimator, least square and weighted least square estimators, maximum product spacing estimators, Cram´er-von Mises estimator and compare those using extensive numerical simulations. Next, we obtain parametric bootstrap confidence interval of the parameter using frequentist approaches. Finally, one real data set has been analysed for illustrative purposes.

Bayesian Estimation ofWarner’s Randomized Response Technique with Transmuted Kumaraswamy Prior

In recent time, the Bayesian approach to randomized response technique has been used for estimating the population proportion especially of respondents possessing sensitive attributes such as induced abortion, tax evasion and shoplifting. This is done by combining suitable prior information about an unknown parameter of the population with the sample information for the estimation of the unknown parameter. In this study, possibility of using a transmuted Kumaraswamy prior is raised, yielding a new Bayes estimator for estimating population proportion of sensitive attribute for Warner’s randomized response technique. Consequently, the proposed Bayes estimator with transmuted Kumaraswamy prior is compared with existing Bayes estimators developed with a simple beta and Kumaraswamy priors in terms of their mean square error. The proposed estimator competes well with the existing estimators for some values of population proportion. The performances of Bayes estimators were also compared using some benchmark data.

Autopoiesis and Its Efficacy—A Metacybernetic View

This paper seeks to explain the nature of autopoiesis and its capacity to be efficacious, and to do this, it uses agency theory as embedded in metacybernetics. Agency, as a generalised intelligent adaptive living system, can anticipate the future once it has internalised a representation of an active contextual situation through autopoiesis. The role of observation and the nature of internalisation will be discussed, explaining that the latter has two states that determine agency properties of cognition. These are assimilation and accommodation. Assimilation is an information process and results in implicit cognition and recognition, whereas accommodation uses assimilated information delivering explicit cognition, recognition, and conscious awareness with rationality. Similarly, anticipation, a required property of the living, has two states, weak and strong, and these correspond to the two states of internalisation. Autopoiesis has various properties identifiable through the lenses of three autonomous but configurable schemas: General Collective Intelligence (GCI), Eigenform, and Extreme Physical Information (EPI). GCI is a pragmatic evolutionary approach concerned with a contextually connected purposeful and relatable set of task processes, each undertaken by a team of subagencies seeking collective fitness. Eigenform is a symbolic approach that is concerned with how observations can be suitably internalised and thus be used as a token to determine future behaviour, and how that which has been internalised can be adopted to anticipate the future. Extreme Physical Information (EPI) is an empirical approach concerned with acquiring information through observation of an unknown parameter through sampling regimes. The paper represents the conceptualisations of each schema in terms of autopoietic efficacy, and explores their configurative possibilities. It will adopt the ideas delivered to enhance explanations of the nature of autopoiesis and its efficacy within metacybernetics, providing a shift in thinking about autopoiesis and self-organisation.

Statistical Inference for Piecewise Affine System Identification

This short note studies the problem of piecewise affine system identification, being a special nonlinear system based on our previous contribution on it. Two different identification strategies are proposed to achieve our mission, such as centralized identification and distributed identification. More specifically, for centralized identification, the total observed input-output data are used to estimate all unknown parameter vectors simultaneously without any consideration on the classification process. But for distributed identification, after the whole observed input-output data are classified into their own right subregions, then part input-output data, belonging to the same subregion, are applied to estimate the unknown parameter vector. Whatever the centralized identification and distributed identification, the final decision is to determine the unknown parameter vector in one linear form, so the recursive least squares algorithm and its modified form with the dead zone are studied to deal with the statistical noise and bounded noise, respectively. Finally, one simulation example is used to compare the identification accuracy for our considered two identification strategies.

On the generalization of the central limit theorem for the least-squares estimator of the unknown parameter in the autoregressive process of order one (AR(1))

In this work it is proved central limit theorem for the least-squares estimator of the unknown parameter in the generalization autoregressive process of order one (AR(1)).

Iterative Data-Driven Control for Closed Loop with Two Unknown Controllers

Iterative idea is combined with data-driven control and is used to design the feedforward controller and feedback controller simultaneously. Consider one closed loop system with two controllers, the classical model-based control holds on the condition of known plant. To alleviate the modeling process for plant, data-driven control is applied to design the two controllers. After these two controllers are parametrized by two unknown parameter vectors, the iterative idea is introduced to identify these two parameter vectors. Furthermore, for more general case of controllers, the closed relations between controllers and expected transfer functions are derived. Then, the iterative idea is also introduced to achieve the controller design. To be of benefit for latter stability analysis, some equities are derived for output-input sensitivity functions with three kinds of disturbances. Generally, after formulating the problem of the controller design as one model-matching problem, the purpose of this paper is threefold. First, we derive that, in case of two parametrized controllers, the iterative idea is performed to identify these two unknown parameter vectors, even when parameters converge to their true values. Second, we show how to design the two controllers iteratively for more general forms and find the closed relations between these controllers and expected closed loop transfer functions. Third, we provide some heuristic considerations on output-input sensitivity functions, which are of benefit for our stability analysis on data-driven control. Finally, one example is given to show the feasibility of our proposed theories.

Controlled Switching Diffusions Under Ambiguity: The Average Criterion

This paper concerns controlled switching diffusions. In particular, we consider that the drift coefficient of the diffusion process depends on an unknown (and possibly nonobservable) parameter. For giving solution to our control problem, we formulate it as a game against nature, where the ambiguity is represented by nature that chooses values of the unknown parameter through actions so playing the role as an opposite player of the controller. Our objective is to give conditions to characterize the ergodic optimality and guarantee the existence of optiaml policies for the central controller. Finally, we provide two examples to illustrate our results.