Coalgebraic Reasoning with Global Assumptions in Arithmetic Modal Logics

We establish a generic upper bound ExpTime for reasoning with global assumptions (also known as TBoxes) in coalgebraic modal logics. Unlike earlier results of this kind, our bound does not require a tractable set of tableau rules for the instance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that potentially avoids building the entire exponential-sized space of candidate states, and thus offers a basis for practical reasoning. This algorithm still involves frequent fixpoint computations; we show how these can be handled efficiently in a concrete algorithm modelled on Liu and Smolka’s linear-time fixpoint algorithm. Finally, we show that the upper complexity bound is preserved under adding nominals to the logic, i.e., in coalgebraic hybrid logic.

Haar wavelet method for solution of variable order linear fractional integro-differential equations

<abstract><p>In this paper, we developed a computational Haar collocation scheme for the solution of fractional linear integro-differential equations of variable order. Fractional derivatives of variable order is described in the Caputo sense. The given problem is transformed into a system of algebraic equations using the proposed Haar technique. The results are obtained by solving this system with the Gauss elimination algorithm. Some examples are given to demonstrate the convergence of Haar collocation technique. For different collocation points, maximum absolute and mean square root errors are computed. The results demonstrate that the Haar approach is efficient for solving these equations.</p></abstract>

Framework of Electrical Fire Probability Estimation Based on Bayesian Network Model Inference

Electrical fire had become one of the main parts in total fire accidents. Most of researches rely on the complex combustion models, which consume a huge number of computational resources. However, few studies focus on evaluating fire disaster by probability theory, and estimate the likelihood of fire occurring by the calculation result of probability based on the current data from the sensor. Bayesian Network is introduced due to the advantage of calculation complexity, ability of expressing uncertain factors and the accuracy of model with incomplete data. Some problems should be solved before using Bayesian Network to inference events based on given evidences. In this paper, the structure and the parameter of the Bayesian Network is created by the discussing result of the experts and scholars in electrical fire research field. A frequently-used fuzzy function called Sigmoid function to process data from raw data to the probability. Inference result by Bayesian Network is calculated by the Variable Elimination algorithm. A case study about the simulation of analyzing the probability of electrical fire happened when the load of circuit is under the high status. Research result shows that Bayesian Network model is suitable for estimating and analyzing in the scenario of electrical fire. Model has a good robust to express probability of electrical fire probability, which is of vital importance for estimating whether the fire occurs or not, thus providing significant information and instruction for preventing electrical fire and the sustainability of the environment. Based on the simulation result, it can conclude that the Bayesian network model inference is suitable for the electrical fire estimation scenario, and the introducing of this scheme is possible for predict electrical fire.

Conceptual Research and Verification of a Single-stage High-precision Pointing Technology

High-precision pointing plays a critical role in optical equipment and laser communication systems. In order to reach the level of sub mrad for pointing accuracy, a two-stage pointing technology is currently widely used. However, this results in significant technical complexity. Therefore, the realization of a high-precision pointing technology under single-stage control is highly challenging. In this study, we find that erase the floating errors of the middle link of the mechanism can effectively improve the pointing accuracy. Based on this assumption, we propose the concept of a single-stage high-precision pointing technology and also establish its mathematical model of drive and an error elimination algorithm. Using modern computer technology, we study the working principle of this single-stage high-precision pointing technology in detail. We also build a prototype and test its performance. The test results show that the uniaxial error of the prototype is no greater than 0.004°, while its spatial synthetic error is no greater than 0.006° and the stability time is less than 100 ms. The test results show that this concept is completely feasible. It is also found that the accuracy of the pointing system can further be improved when the vibration is suppressed, which also represents an important concept for further research. We anticipate that an ultra-high-precision pointing system with single-stage control will be established in the near future.

Development and Validation of a Novel Risk Prediction Model Using Recursive Feature Elimination Algorithm for Acute-on-Chronic Liver Failure in Chronic Hepatitis B Patients With Severe Acute Exacerbation

Background: Patients with chronic hepatitis B (CHB) with severe acute exacerbation (SAE) are at a progression stage of acute-on-chronic liver failure (ACLF) but uniform models for predicting ACLF occurrence are lacking. We aimed to present a risk prediction model to early identify the patients at a high risk of ACLF and predict the survival of the patient.Methods: We selected the best variable combination using a novel recursive feature elimination algorithm to develop and validate a classification regression model and also an online application on a cloud server from the training cohort with a total of 342 patients with CHB with SAE and two external cohorts with a sample size of 96 and 65 patients, respectively.Findings: An excellent prediction model called the PATA model including four predictors, prothrombin time (PT), age, total bilirubin (Tbil), and alanine aminotransferase (ALT) could achieve an area under the receiver operating characteristic curve (AUC) of 0.959 (95% CI 0.941–0.977) in the development set, and AUC of 0.932 (95% CI 0.876–0.987) and 0.905 (95% CI 0.826–0.984) in the two external validation cohorts, respectively. The calibration curve for risk prediction probability of ACLF showed optimal agreement between prediction by PATA model and actual observation. After predictive stratification into different risk groups, the C-index of predictive 90-days mortality was 0.720 (0.675–0.765) for the PATA model, 0.549 (0.506–0.592) for the end-stage liver disease score model, and 0.648 (0.581–0.715) for Child–Turcotte–Pugh scoring system.Interpretation: The highlypredictive risk model and easy-to-use online application can accurately predict the risk of ACLF with a poor prognosis. They may facilitate risk communication and guidetherapeutic options.

THEORETICAL AND COMPUTATIONAL RESULTS FOR MIXED TYPE VOLTERRA–FREDHOLM FRACTIONAL INTEGRAL EQUATIONS

In this paper, we develop a numerical method for the solutions of mixed type Volterra–Fredholm fractional integral equations (FIEs). The proposed algorithm is based on Haar wavelet collocation technique (HWCT). Under certain conditions, we prove the existence and uniqueness of the solution. Also, some stability results are given of Hyers–Ulam (H–U) type. With the help of the HWCT, the considered problem is transformed into a system of algebraic equations which is then solved for the required results by using Gauss elimination algorithm. Some numerical examples for convergence of the proposed technique are taken from the literature. Maximum absolute and root mean square errors are calculated for different collocation points (CPs). The results show that the HWCT is an effective method for solving FIEs. The convergence rate for different CPS is also calculated, which is nearly equal to 2.

Gaussian Elimination versus Greedy Methods for the Synthesis of Linear Reversible Circuits

Linear reversible circuits represent a subclass of reversible circuits with many applications in quantum computing. These circuits can be efficiently simulated by classical computers and their size is polynomially bounded by the number of qubits, making them a good candidate to deploy efficient methods to reduce computational costs. We propose a new algorithm for synthesizing any linear reversible operator by using an optimized version of the Gaussian elimination algorithm coupled with a tuned LU factorization. We also improve the scalability of purely greedy methods. Overall, on random operators, our algorithms improve the state-of-the-art methods for specific ranges of problem sizes: The custom Gaussian elimination algorithm provides the best results for large problem sizes (n > 150), while the purely greedy methods provide quasi optimal results when n < 30. On a benchmark of reversible functions, we manage to significantly reduce the CNOT count and the depth of the circuit while keeping other metrics of importance (T-count, T-depth) as low as possible.