Unknown Values Research Articles

Solving Conditional Linear Recurrences for Program Verification: The Periodic Case

In program verification, one method for reasoning about loops is to convert them into sets of recurrences, and then try to solve these recurrences by computing their closed-form solutions. While there are solvers for computing closed-form solutions to these recurrences, their capabilities are limited when the recurrences have conditional expressions, which arise when the body of a loop contains conditional statements. In this paper, we take a step towards solving these recurrences. Specifically, we consider what we call conditional linear recurrences and show that given such a recurrence and an initial value, if the index sequence generated by the recurrence on the initial value is what we call ultimately periodic, then it has a closed-form solution. However, checking whether such a sequence is ultimately periodic is undecidable so we propose a heuristic "generate and verify" algorithm for checking the ultimate periodicity of the sequence and computing closed-form solutions at the same time. We implemented a solver based on this algorithm, and our experiments show that a straightforward program verifier based on our solver and using the SMT solver Z3 is effective in verifying properties of many benchmark programs that contain conditional statements in their loops, and compares favorably to other recurrence-based verification tools. Finally, we also consider extending our results to computing closed-form solutions of recurrences with unknown initial values.

Strict inequalities for the n-crossing number

In 2013, Adams introduced the [Formula: see text]-crossing number of a knot [Formula: see text], denoted by [Formula: see text]. Inequalities between the [Formula: see text]-, [Formula: see text]-, [Formula: see text]- and [Formula: see text]-crossing numbers have been previously established. We prove [Formula: see text] for all knots [Formula: see text] that are not the trivial, trefoil, or figure-eight knot. We show this inequality is optimal and obtain previously unknown values for [Formula: see text].

Finding the Best Dueler

Consider a set of n players. We suppose that each game involves two players, that there is some unknown player who wins each game it plays with a probability greater than 1/2, and that our objective is to determine this best player. Under the requirement that the policy employed guarantees a correct choice with a probability of at least some specified value, we look for a policy that has a relatively small expected number of games played before decision. We consider this problem both under the assumption that the best player wins each game with a probability of at least some specified value p0>1/2, and under a Bayesian assumption that the probability that player i wins a game against player j is vivi+vj, where v1,…,vn are the unknown values of n independent and identically distributed exponential random variables. In the former case, we propose a policy where chosen pairs play a match that ends when one of them has had a specified number of wins more than the other; in the latter case, we propose a Thompson sampling type rule.

A three-way decision model on incomplete single-valued neutrosophic information tables

In this paper, we focus on the three-way decision model on incomplete single-valued neutrosophic information tables. Firstly, we define the minimum and maximum similarity measures between single-valued neutrosophic numbers (SVNNs) which may contain unknown values. On this basis, the notion of θ-weak similarity measure is given. Then, we introduce the conception of an incomplete single-valued neutrosophic information table (ISVNIT). For an incomplete single-valued neutrosophic information table, a new similarity relation is proposed based on the θ-weak similarity measure. Some properties are also studied. By using Bayesian decision theory and this similarity relation, we construct a three-way decision model on an ISVNIT. Finally, an example of choosing product service providers is explored to illustrate the rationality and feasibility of the proposed model. We also discuss the influence of parameters in the model on decision results.

Shortest Confidence Intervals for Weibull Modulus for Small Samples in Materials Reliability Analysis

The Weibull distribution has been widely used to model strength properties of brittle materials. Estimation of confidence intervals for Weibull shape parameter has been an important concern, since small sample sizes in materials science experiments bring about large intervals. Many methods have been proposed in the literature for constructing shorter intervals; the methods of maximum likelihood, least square, and Menon are among the most extensively studied methods. However, they all use an equal-tails approach. The pivotal quantities used for constructing confidence intervals have right-skewed and unimodal distributions, thus, they clearly do not produce the shortest intervals for a given confidence level in equal tail form. This study constructs the shortest confidence intervals for the three aforementioned methods and compares their performances by their equal-tails counterparts. To this end, a comprehensive simulation study has been conducted for the shape parameter values between 1 to 80 and the sample sizes between 3 to 20. The comparison criterion is chosen as the expected interval length. The results show that the shortest confidence intervals in each of three methods have yielded considerably narrower intervals. Further, the unknown parameter values are more centered in these intervals.

Contributions from experimental geostatistical analyses for solving the cloud-cover problem in remote sensing data

Nowadays, in many fields and applications, such as mining engineering, environmental monitoring, soil science, natural resources and environmental topics, the potential of Remote Sensing have been exploited. Large amount of data, easy and fast accessibility, and time–space availability are the reasons of attractiveness of satellite data in many fields of geosciences. However, satellite images face the problems due to presence of shadows and clouds, which is a general and real challenge since the surface features are masked. In many cases, a dense cloud cover simply prevents any detailed study of the target area through Earth Observation techniques. Geostatistics is a science field properly developed to estimate the unknown values in two-dimensional or three-dimensional space; therefore, it can be a potential approach to solve cloud-cover issues in Remote Sensing investigations. This work applies the geostatistical tools over a sentinel-2 satellite image targeting land cover in Emilia Romagna (Italy). The three main spectrum bands (RGB-values) with 10-m spatial resolution have been selected as target variables. The objective is to estimate pixel values within an area which is covered by clouds. The spatial variability of pixels with available land cover information have been studied through the use of variogram tools. Different estimation neighborhoods have been tested for application of the Kriging interpolation method, in order to estimate the RGB values below the cloud-covered area. The estimation has been performed, by controlling the properties of the estimator, the varying sizes and shapes of the neighborhood, the available number of RGB data used for estimation and the spatial distribution of pixels in the image. An image with close time period, without clouds, has been used to validate the results. Moreover, the estimation variance of RGB values for each pixel has been mapped. Results have shown the advantages and limitations of the proposed geostatistical method for the specific application of cloud-covered areas.

COMPUTATIONAL INTELLIGENCE METHODS TO PATIENTS STRATIFICATION IN THE MEDICAL MONITORING SYSTEMS

Context. In modern medical practice the automation and information technologies are increasingly being implemented for diagnosing diseases, monitoring the condition of patients, determining the treatment program, etc. Therefore, the development of new and improvement of existing methods of the patient stratification in the medical monitoring systems is timely and necessary.
 Objective. The goal of intelligent diagnostics of patient’s state in the medical monitoring systems – reducing the likelihood of adverse states based on the choice of an individual treatment program:
 − reducing the probability of incorrectly determining the state of the patients when monitoring patients;
 − obtaining stable effective estimates of unknown values of treatment actions for patients (corresponding to the found state);
 − the choice of a rational individual treatment program for the patients, identified on the basis of the forecasted state.
 Method. Proposed methodology, which includes the following computational intelligence methods to patient’s stratification in the medical monitoring systems:
 1) method of cluster analysis based on the agent-based approach – the determination of the possible number of patient’s states using controlled variables of state;
 2) method of robust metamodels development by means artificial neuron networks under a priori data uncertainty (only accuracy of measurements is known) in the monitoring data: a) a multidimensional logistic regression model in the form of analytical dependences of the posterior probabilities of different states of the patients on the control and controlled variables of state; b) a multidimensional diagnostic model in the form of analytical dependences of the objective functions (quality criteria of the patient’s state) on the control and controlled variables of state;
 3) method of estimating informativeness controlled variables of state at a priori data uncertainty;
 4) method of robust multidimensional models development for the patient’s state control under a priori data uncertainty in the monitoring data in the form of analytical dependencies predicted from the measured values of the control and controlled variables of state in the monitoring process;
 5) method of reducing the controlled state variables space dimension based on the analysis of the variables informativeness of the robust multidimensional models for the patient’s state control;
 6) method of patient’s states determination based on the classification problem solution with the values of the control and forecasted controlled variables of state with using the probabilistic neural networks;
 7) method of synthesis the rational individual patient’s treatment program in the medical monitoring system, for the state identified on the basis of the forecast.
 Proposed the structure of the model for choosing the rational individual patient’s treatment program based on IT Data Stream Mining, which implements the «Big Data for Better Outcomes» concept.
 Results. The developed advanced computational intelligence methods for forecast states were used in choosing the tactics of treating patients, to forecast treatment complications and assess the patient’s curability before and during special treatment.
 Conclusions. Experience in the implementation of “Big Data for Better Outcomes” concept for the solution of the problem of computational models for new patient stratification strategies is presented. Advanced methodology, computational methods for a patient stratification in the medical monitoring systems and applied information technology realizing them have been developed. The developed methods for forecast states can be used in choosing the tactics of treating patients, to forecast treatment complications and assess the patient’s curability before and during special treatment.

Estimation of Chlorine Concentration in Water Distribution Systems Based on a Genetic Algorithm

This paper proposes a methodology based on a genetic algorithms (GA) to calibrate the parameters of a chlorine decay model in a water distribution system (WDS). The proposed methodology first contemplates that a GA is implemented using historical measurements of chlorine concentration at some sensed nodes to calibrate the unknown values corresponding to both the bulk and wall reaction coefficients. Once both parameters are estimated, the optimal-fit chlorine decay model is used to predict the decay of chlorine concentration in the water at each node for any concentration input at the pumping station. Then, a second GA-based algorithm is implemented to obtain the minimal chlorine concentration needed at the input to ensure that every node in the system meets the official normativity requirements for free chlorine in a WDS. The proposed methodology performed satisfactorily for a WDS simulated in EPANET with a GA implemented in MATLAB, both for the estimation of the reaction coefficients and the optimization of the required chlorine concentration at the input. Simulation results illustrate the performance of the proposed algorithm.

Parameter Estimation Analysis in a Model of Honey Production

Honeybee losses are an extensive global problem. In this study, a new compartment model of honeybee population that mainly concerns honey production is developed. The model describes the interaction of the food stock with the brood (immature bees), adult bees and produced honey. In the present paper, the issue of an adequate model recovery is addressed and the parameter identification inverse problem is solved. An adjoint equation procedure to obtain the unknown parameter values by minimizing the functional error during a period of time is proposed. Numerical simulations with realistic data are discussed.

Multicollinearity applied stepwise stochastic imputation: a large dataset imputation through correlation-based regression

This paper presents a stochastic imputation approach for large datasets using a correlation selection methodology when preferred commercial packages struggle to iterate due to numerical problems. A variable range-based guard rail modification is proposed that benefits the convergence rate of data elements while simultaneously providing increased confidence in the plausibility of the imputations. A large country conflict dataset motivates the search to impute missing values well over a common threshold of 20% missingness. The Multicollinearity Applied Stepwise Stochastic imputation methodology (MASS-impute) capitalizes on correlation between variables within the dataset and uses model residuals to estimate unknown values. Examination of the methodology provides insight toward choosing linear or nonlinear modeling terms. Tailorable tolerances exploit residual information to fit each data element. The methodology evaluation includes observing computation time, model fit, and the comparison of known values to replaced values created through imputation. Overall, the methodology provides useable and defendable results in imputing missing elements of a country conflict dataset.

Investigation of the inverse problem for the Arrhenius equation using the example of thermal degradation of spongin-based scaffolds

A mathematical description of the thermal degradation of spongin-based scaffolds is given. The Arrhenius integral was evaluated using the inverse problem approach, in which the unknown values were the activation energy EA, the pre-exponential factor A, and the model function f(α) characterizing the physical process. The form of f(α) was determined and the values of the parameters EA, A and TS were evaluated in detail. Moreover, the function f(α) assessed in this study was compared with classical solid-state model functions. Finally, the mean square minimization approach was used to solve the inverse problem with unknown function f(α) and pre-exponential constant A. Likewise, the approximation of f(α) with 6th- and 7th-degree polynomials was used to obtain numerical values of EA and A. This study evaluated the inverse problem approach for the Arrhenius equation. These investigations provide new insight into the description of the thermal degradation of spongin-based scaffolds.

Optimal Parameter Estimation of Solar Photovoltaics Through Nature Inspired Metaheuristic and Hybrid Approaches

Estimation of solar photovoltaic (PV) equivalent model parameters through the manufacturer's datasheet or experimental performance current voltage (I-V) characteristics is an apprehension among researchers. In this paper, two approaches are instigated and compared i.e. metaheuristic pheromone value black widow optimisation (pv-BWO) and hybrid sailfish optimisation (h-SFO) for the estimation of a single-diode model (SDM) and double-diode model (DDM) parameters for the accurate solar PV modelling. Four distinct case studies that incorporate four different PV modules i.e. RTC France, PWP 201, SHARP ND-R250A5, and EIL 75W PV are investigated, where the validation of the proposed methods is carried out through the experimental performance characteristics of solar PV under test i.e. the I-V and power-voltage (P-V) performance characteristics. Moreover, the performance is evaluated on various error functions, and experimental I-V and P-V characteristics, where the results are also compared with the various techniques of parameter estimation in the literature. It is important to underline that the closeness of the objective function to zero exhibits the congruence of estimated parameters with the exact parameters, where the exact parameter value is not accessible. Therefore, the preciseness rests on the experimental data only, where any significant reduction in OF i.e. RMSE considered as an improvement towards the exactness of real unknown parameter values. The pv-BWO exhibits an average of 69.89% of lower error results when compared with few existing methods, whereas h-SFO recorded a higher RMSE of about 93% when compared with the pv-BWO which suggests the suitability of pv-BWO over h-SFO and few existing methods.

Identification of tissue and therapy parameters from surface temperature.

The temperature distribution of human body tissues, when electromagnetic waves are applied, is studied with the help of the bioheat equation, which is characterised by several thermal parameters, such as thermal conductivity, perfusion frequency or metabolic heat. There are also electromagnetic parameters, such as electrical conductivity and dielectric constant. Besides, therapy parameters, such as the applied power should be considered. If the values of all these parameters are known, the time evolution of the temperature can be determined. Some of these values can be found in specialised databases, and others are unknown but approximate values can be obtained by reasonable estimations. The outcome of simulations depends heavily on the parameter values. Surface temperature helps in providing better estimates of the parameter values. Once these parameters are identified, medical analyses can be performed to assess the dosimetry of the radiation so that it does not damage tissues, for example. The surface temperature is obtained from a sequence of thermographic images. Based on these experimental data, an algorithm is applied to find the values of the needed parameters. The model is simulated iteratively, adjusting the parameters at each step, reducing the approximation error between the simulation and the data. This is an optimization problem that belongs to the realm of inverse problems. It can be solved using techniques based on the gradient concept, however, this problem can be ill-conditioned, so probabilistic or evolutionary algorithms are also used. In this paper, the simulation is made using a method based on Legendre wavelets. It is proposed that the subsequent optimization is made using an evolutionary algorithm, that has shown great robustness in the problems where it has been applied. As far as known, it has never been applied to the bioheat equation. This is the aim of this work.

Upper and lower bounds on delta-crossing number and tabulation of knots up to four delta-crossings

In this paper, we will strengthen the known upper and lower bounds on the delta-crossing number of knots in terms of the triple-crossing number. The latter bound turns out to be strong enough to obtain unknown values of triple-crossing numbers for a few knots. We also prove that we can always find at least one tangle from a particular set of four tangles, in any triple-crossing projections of any non-trivial knot or non-split link. In the last section, we enumerate and generate tables of minimal delta-diagrams for all prime knots up to the delta-crossing number equal to four. We also give a concise survey about known inequalities between integer-valued classical knot invariants.

Soliton solutions of the (2+1)-dimensional Kadomtsev–Petviashvili equation via two different integration schemes

In this research paper, we take into account the ([Formula: see text])-dimensional Kadomtsev–Petviashvili equation which is important in the soliton theory of nonlinear physics. To get the desired soliton solutions, the modified F-expansion method using the Riccati equation which has many solution functions, as well as the modified generalized Kudryashov’s method, had been effectively implemented. One of the reasons for the preference of the methods is that the proposed methods have been widely used before and they have not been applied to this problem. First, the wave transform is applied to the considered nonlinear partial differential equation (NLPDE), the nonlinear ordinary differential equation (NODE) form and the balancing constant are determined. The next step is to use the auxiliary equation depending on the proposed method to find the solution of the NODE form and to obtain the linear algebraic equation system. The solution of this system gives different solution sets for unknown parameter values. Then, soliton solution functions are constructed by using the suitable solution sets. After testing and confirming that the obtained solution functions satisfy the main equation, the three- and two-dimensional illustrations are depicted.

Nuclear analysis method based on current coupling neutron response reconstruction method

ABSTRACT The current coupling neutron response reconstruction method has been developed, based on the already developed direct response matrix method. In the current coupling neutron response reconstruction method, by setting fuel rod neutron production rates as new unknown values, the need to calculate the response matrix is eliminated, and the calculation time can be reduced compared to the direct response matrix method. Furthermore, by evaluating the neutron fluxes and the cross sections using the reconstruction method of homogenized cross sections which has already been developed, the neutron effective multiplication factor is directly evaluated from the reaction rate ratio, and convergence can be improved. For the purpose of verification, calculations for heterogeneous systems were performed. The results obtained using the current coupling neutron response reconstruction method agreed well with those obtained using direct calculations by the Monte Carlo method, and they were almost the same as those obtained using the direct response matrix method. These good agreements with the direct calculations using the Monte Carlo method meant that the current coupling neutron response reconstruction method accurately reflected the effects of intra- and inter-assembly heterogeneities. In terms of calculation time, the current coupling neutron response reconstruction method was 33 to 60 times faster than the direct response matrix method by eliminating the need for a response matrix and improving convergence.

High-precision deformation analysis of yingxian wooden pagoda based on UAV image and terrestrial LiDAR point cloud

The monitoring of wooden pagodas is a very important task in the restoration of wooden pagodas. Traditionally, this labor has always been carried out by surveying personnel, who manually check all parts of the pagoda, which not only consumes huge manpower, but also suffers from low efficiency and measurement errors. This article evaluates the feasibility of combining portable 3D light detection and ranging (LiDAR) scanning and unmanned aerial vehicle (UAV) photogrammetry to perform these inspection tasks easily and accurately. The wooden pagoda's exterior picture and inside point cloud are acquired using a UAV and a LiDAR scanner, respectively. We propose a feature−based global alignment method to register the site point cloud. The error equation of the column of observed values is utilized as the beginning value of the feature constraint for global leveling. The beam method leveling model solves the spatial transformation parameters and the unknown point leveling values. Then, the Structure from Motion (SfM) algorithm of computer vision is used to realize the fusion of the dense point cloud of the exterior of the wooden pagoda generated from multiple non−measured images by global optimization and the LiDAR point cloud of the interior of the wooden pagoda to obtain the complete point cloud of the wooden pagoda, which makes the deformation monitoring of the pagoda more detailed and comprehensive. After experimental verification, the overall registration accuracy of the Yingxian wooden pagoda reaches 0.006 m. Compared with the scanning point cloud data in 2018, the model is more accurate and complete. By analyzing and comparing the data of the second floor of the wooden pagoda, we knew that the inclination of a second bright layer and a second dark layer is still developing steadily. Overall, the western outer trough inclines thoughtfully, and the column frame slopes from southwest to northeast. Some internal columns showed a negative offset in 2020, and the deformation analysis of a single column was realized by comparing it with the standard column model. The main contribution of this method lies in the effective integration of UAV images and point cloud data to provide accurate data sources for good modeling. This research will provide theoretical and methodological support for the digital protection of architectural heritage and GIS data modeling. The analysis results can provide a scientific basis for the restoration scheme design.

Predictive Modeling and Analytics for Diabetes using Hyperparameter tuned Machine Learning Techniques

Accuracy of a classifier is important for the success of any prediction model. The more accuracy a classifier possesses, the more robust the system is made on it. In this paper, a disease prediction model is developed in Python for the classification of diabetes in patients. In the research paper, study is performed to make a comparative analysis of the performance of machine learning classification algorithms. The classifier's performances are enhanced by of tuning the hyperparameters of classifiers and applied different dataset preprocessing methods. In this experimental analysis, four models have been created, and each model is based on a dataset, obtained by different preprocessing methods of PIMA dataset. For each model, K-Nearest Neighbors, Decision Tree, Random Forest, and Support vector machines classification algorithms, have been applied and classifier's hyperparameters are tuned to get better results from these models.A detail analysis has also performed to get the best prediction model, the best classifier and effective preprocessing methods for it. The prediction model use F1score as the main metric. The highest F1score and accuracy are 75.68 % and 88.61% respectively, which is achieved by Random Forest classifier for dataset model D3 obtained by removing the samples having missing or unknown values from PIMA dataset.

Using Dictionary Matching to Improve the Accuracy of MOLLI Myocardial T1 Analysis and Measurements of Heart Rate Variability.

We analyzed modified Look-Locker inversion recovery (MOLLI) T1 measurements by applying a dictionary matching strategy and aimed to acquire T1 measurements more accurately than those acquired by the conventional three-parameter matching analysis. We particularly clarified the robustness of this method for measuring heart rate (HR) variability. A phantom experiment using a 3T MRI system was performed for various HRs. The ideal MOLLI signal corresponding to the scan parameter in the MRI experiment was simulated over a wide range of T1 values according to the dictionary. The unknown T1 values were determined by finding the simulated signals in the dictionary corresponding to the measured signals using pattern matching. The measured T1 values showed that the proposed analysis improved the accuracy of T1 measurements compared to those acquired by traditional analysis by up to 10%. In addition, the variability of measurements at several HRs was reduced by up to 100 ms.

Проблема оценки точности параметров цунамиактивности

The subject of the article is the theoretical development of the probabilistic model for a Poisson-type tsunami sequence that is consistent with data on the manifestations of historical events, in order to obtain estimates of the accuracy of the tsunami activity parameters. An example of a tsunami recurrence function, which is the most important quantitative characteristic of tsunami activity for the Port of Malokurilskoye, one of the places in the South Kuril Islands region with the most reliable tsunami height dataset, was created on the basis of a theoretical essay. An explanation for the weak statistical stability of all large values of the tsunami heights, especially for the largest one in the series of observations, was given based on the probability density functions of the ranked tsunami heights. In particular, it means, for example, that the maximum tsunami height recorded at a certain location during a 30-year observation period should be correlated with a wide range of possible recurrence periods of about 10 to 100 years. Synthetic catalogs of the tsunami heights, built for the Port of Malokurilskoye, showed that the tsunami height datasets with a duration of at least 250 or 500 years without gaps are needed to obtain the tsunami activity parameters with an acceptable accuracy of 10 or 5 %. The most important results are the analytical equations for the variances of estimates of the tsunami activity parameters, which characterize the accuracy of these estimates, depending on a priori unknown values of the tsunami activity parameters and the amount of data used.