Search results for: generalization rule

Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: Amir Deljoo

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The endeavor to comprehend the existence have been the center of thought for human in form of different disciplines and now basically in physics as the theory of everything. Here, after a brief review of the basic frameworks of thought, and a history of thought since ancient up to present, a logical methodology is presented based on a core axiom after which a function, a proto-field and then a coordinates are explained. Afterwards a generalization to Standard Model is proposed as General Standard Model which is believed to be the base of the Unified Theory of Everything.

Keywords: general relativity, grand unified theory, quantum mechanics, standard model, theory of everything

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Authors: Giorgio Visentin, Inna S. Kalinina, Alexei A. Buchachenko

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In the ambit of intermolecular interactions, a combination rule is defined as a relation linking a potential parameter for the interaction of two unlike species with the same parameters for interaction pairs of like species. Some of their most exemplificative applications cover the construction of molecular dynamics force fields and dispersion-corrected density functionals. Here, an extended combination rule is proposed, relating the dipole-dipole dispersion coefficients for the interaction of like target species to the same coefficients for the interaction of the target and a set of partner species. The rule can be devised in two different ways, either by uniform discretization of the Casimir-Polder integral on a Gauss-Legendre quadrature or by relating the dynamic polarizabilities of the target and the partner species. Both methods return the same system of linear equations, which requires the knowledge of the dispersion coefficients for interaction between the partner species to be solved. The test examples show a high accuracy for dispersion coefficients (better than 1% in the pristine test for the interaction of Yb atom with rare gases and alkaline-earth metal atoms). In contrast, the rule does not ensure correct monotonic behavior of the dynamic polarizability of the target species. Acknowledgment: The work is supported by Russian Science Foundation grant # 17-13-01466.

Keywords: combination rule, dipole-dipole dispersion coefficient, Casimir-Polder integral, Gauss-Legendre quadrature

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Authors: Chin Ku, Han liang Lin

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The purpose of this study is to visualize how the rule related to urban design influences the building form by 3D modeling software CityEngine. In order to make the goal of urban design clearly connect to urban form, urban planner or designer should understand how the rule affects the form, especially the building form. In Taiwan, the rule pertained to urban design includes traditional zoning, urban design review and building codes. However, zoning cannot precisely expect the outcome of building form and lack of thinking about public realm and 3D form. In addition to that, urban design review is based on case by case, do not have a comprehensive regulation plan and the building code is just for general regulation. Therefore, rule cannot make the urban form reach the vision or goal of the urban design. Consequently, another kind of zoning called Form-based code (FBC) has arisen. This study uses the component of FBC which pertained to urban fabric such as street width, block and plot size, etc., to be the variants of building form, and find out the relationship between the rule and building form. There are three stages of this research, it will start from a field survey of Taichung City in Taiwan to induce the rule-building form relationship by using cluster analysis and descriptive Statistics. Second, visualize the relationship through the parameterized and codified process in CityEngine which is the procedural modeling, and can analyze, monitor and visualize the 3D world. Last, compare the CityEngine result with real world to examine how extent do this model represent the real world appearance.

Keywords: 3D visualization, CityEngine, form-based code, urban form

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Authors: Noura Al-Ajmi, Mohammed A. Almulla

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With the increased utilization of technology devices around the world, healthcare and medical diagnosis are critical issues that people worry about these days. Doctors are doing their best to avoid any medical errors while diagnosing diseases and prescribing the wrong medication. Subsequently, artificial intelligence applications that can be installed on mobile devices such as rule-based expert systems facilitate the task of assisting doctors in several ways. Due to their many advantages, the usage of expert systems has increased recently in health sciences. This work presents a backward rule-based expert system that can be used for a headache diagnosis and medication recommendation system. The structure of the system consists of three main modules, namely the input unit, the processing unit, and the output unit.

Keywords: headache diagnosis system, prescription recommender system, expert system, backward rule-based system

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Authors: Abd El Hady N. Ebraheim

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This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.

Keywords: exponentiated, inversion method, maximum likelihood estimation, transmutation map

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Authors: Alireza Tavakoli Nia

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In order to understand the role of the injured party's fault in dividing liability, we studied its historical background. In common law, the traditional contributory negligence rule was a complete defense. Then the legislature and judicial procedure modified that rule to one of apportionment. In Islamic law, too, the Action rule was at first used when the injured party was the sole cause, but jurists expanded the scope of this rule, so this rule was used in cases where both the injured party's fault and that of the other party are involved. There are some popular approaches for apportionment of damages. Some common law countries like Britain had chosen ‘the causal potency approach’ and ‘fixed apportionment’. Islamic countries like Iran have chosen both ‘the relative blameworthiness’ and ‘equal apportionment’ approaches. The article concludes that both common law and Islamic law believe in the division of responsibility between a wrongdoer claimant and the defendant. In contrast, in the apportionment of responsibility, Islamic law mostly believes in equal apportionment that is way easier and saves time and money, but common law legal systems have chosen the causal potency approach, which is more complicated than the rival approach but is fairer.

Keywords: contributory negligence, tort law, damage apportionment, common law, Islamic law

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Authors: Kim Michelle Siegling, Thomas Spengler, Sebastian Herzog

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In personnel economics, the choice of a leadership style is about the question of how a supervisor should lead his or her employees in such a way that operational goals are achieved. In this paper, it is assumed that such leadership decisions are made according to the situation. Thus, the optimal or at least a permissible leadership style has to be selected from a set of several possible leadership styles. For this choice, a wide range of models has been developed in the scientific literature, from which the so-called normative decision model will be picked out and focused on. While the original model is based on univocal rules, this paper develops a fuzzy rule system.

Keywords: leadership, leadership styles, rule based systems, fuzzy logic

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Authors: Mehdi Rashidi-Kouchi, Asghar Rahimi

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Sun introduced a generalization of frames and showed that this includes more other cases of generalizations of frame concept and proved that many basic properties can be derived within this more general context. Another generalization of frames is frames in Hilbert C*-module. It has been proved that every g-frame in Hilbert space H respect to Hilbert space K is a frame for B(H;K) as Hilbert C*-module. We show that every g-Riesz basis for Hilbert space H respect to K by add a condition is a Riesz basis for Hilbert B(K)-module B(H;K). Also, we investigate similar result for g-orthonormal and orthogonal bases.

Keywords: frame, g-frame, Riesz basis, g-Riesz basis, Hilbert C*-module

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Authors: Mahdiyeh Abbasi, Akbar Golchin

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It is well-known that, using principal weak flatness property, some important monoids are characterized, such as regular monoids, left almost regular monoids, and so on. In this article, we define a generalization of principal weak flatness called GP-Flatness, and will characterize monoids by this property of their right (Rees factor) acts. Also we investigate new classes of monoids called generally regular monoids and generally left almost regular monoids.

Keywords: G-left stabilizing, GP-flatness, generally regular, principal weak flatness

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Authors: T. Bouchabchoub, A. Bendahmane, A. Haouriqui, N. Attou

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This paper presents simulation results of Forex predicting model equations in order to give approximately a prevision of interest rates. First, Hall-Taylor (HT) equations have been used with Taylor rule (TR) to adapt them to European and American Forex Markets. Indeed, initial Taylor Rule equation is conceived for all Forex transactions in every States: It includes only one equation and six parameters. Here, the model has been used with Hall-Taylor equations, initially including twelve equations which have been reduced to only three equations. Analysis has been developed on the following base macroeconomic variables: Real change rate, investment wages, anticipated inflation, realized inflation, real production, interest rates, gap production and potential production. This model has been used to specifically study the impact of an inflation shock on macroeconomic director interest rates.

Keywords: interest rate, Forex, Taylor rule, production, European Central Bank (ECB), Federal Reserve System (FED).

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Authors: Babatunde J. Falaye

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In this study, we obtain the approximate analytical solutions of the radial Schrödinger equation for the Deng-Fan diatomic molecular potential by using exact quantization rule approach. The wave functions have been expressed by hypergeometric functions via the functional analysis approach. An extension to rotational-vibrational energy eigenvalues of some diatomic molecules are also presented. It is shown that the calculated energy levels are in good agreement with the ones obtained previously E_nl-D (shifted Deng-Fan).

Keywords: Schrödinger equation, exact quantization rule, functional analysis, Deng-Fan potential

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Authors: M. A. Sedghamiz, S. Raeissi

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This study presents three different approaches to estimate bubble point pressures for the binary system of CO2 and ethyl palmitate fatty acid ethyl ester. The first method involves the Peng-Robinson (PR) Equation of State (EoS) with the conventional mixing rule of Van der Waals. The second approach involves the PR EOS together with the Wong Sandler (WS) mixing rule, coupled with the Uniquac Ge model. In order to model the bubble point pressures with this approach, the volume and area parameter for ethyl palmitate were estimated by the Hansen group contribution method. The last method involved the Peng-Robinson, combined with the Wong-Sandler Method, but using NRTL as the GE model. Results using the Van der Waals mixing rule clearly indicated that this method has the largest errors among all three methods, with errors in the range of 3.96–6.22 %. The Pr-Ws-Uniquac method exhibited small errors, with average absolute deviations between 0.95 to 1.97 percent. The Pr-Ws-Nrtl method led to the least errors where average absolute deviations ranged between 0.65-1.7%.

Keywords: bubble pressure, Gibbs excess energy model, mixing rule, CO2 solubility, ethyl palmitate

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Authors: Deretha Bester

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This research employs a theoretical framework to investigate the interplay between factors that lead from predatory governance and predatory rule to military coups, utilizing the frustration-aggression theory as its guiding lens. It adopts a case-oriented approach and employs thematic analysis to examine the socio-economic, governance, and political environment that precipitated the August 2020 Malian military coup. Presenting seven key themes, it reveals how predatory rule and its manifestation in the Malian context was a critical factor in paving the way for the military coup. The study provides critical reflections into the historical, regional, and political dynamics reshaping Africa’s changing political landscape. It presents a conceptual model to comprehend how predatory governance fosters conditions favorable for military coups. Insights from the Malian case study offer valuable perspectives for analyzing events in comparable contexts. This understanding is crucial for grasping the precursors and impact of predatory rule and popular frustrations in contexts where military coups emerge.

Keywords: predatory rule, military coups, socio-political analysis, frustration-aggression theory, Mali

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Authors: Wael Bakhit, Salma Bakhit

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This paper employs a quarterly time series to determine the timing of structural breaks for interest rates in USA over the last 60 years. The Chow test is used for investigating the non-stationary, where the date of the potential break is assumed to be known. Moreover, an empirical examination of the financial sector was made to check if it is positively related to deviations from an assumed interest rate as given in a standard Taylor rule. The empirical analysis is strengthened by analysing the rule from a historical perspective and a look at the effect of setting the interest rate by the central bank on financial imbalances. The empirical evidence indicates that deviation in monetary policy has a potential causal factor in the build-up of financial imbalances and the subsequent crisis where macro prudential intervention could have beneficial effect. Thus, our findings tend to support the view which states that the probable existence of central banks has been a source of global financial crisis since the past decade.

Keywords: Taylor rule, financial imbalances, central banks, econometrics

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Authors: M. Pramila Devi, N. V. N. Indra Kiran

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Control charts, predominantly in the form of X-bar chart, are important tools in statistical process control (SPC). They are useful in determining whether a process is behaving as intended or there are some unnatural causes of variation. A process is out of control if a point falls outside the control limits or a series of point’s exhibit an unnatural pattern. In this paper, a study is carried out on four training algorithms for CCPs recognition. For those algorithms optimal structure is identified and then they are studied for type I and type II errors for generalization without early stopping and with early stopping and the best one is proposed.

Keywords: control chart pattern recognition, neural network, backpropagation, generalization, early stopping

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Authors: Salima Smiti, Ines Gasmi, Makram Soui

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Credit risk is the most important issue for financial institutions. Its assessment becomes an important task used to predict defaulter customers and classify customers as good or bad payers. To this objective, numerous techniques have been applied for credit risk assessment. However, to our knowledge, several evaluation techniques are black-box models such as neural networks, SVM, etc. They generate applicants’ classes without any explanation. In this paper, we propose to assess credit risk using rules classification method. Our output is a set of rules which describe and explain the decision. To this end, we will compare seven classification algorithms (JRip, Decision Table, OneR, ZeroR, Fuzzy Rule, PART and Genetic programming (GP)) where the goal is to find the best rules satisfying many criteria: accuracy, sensitivity, and specificity. The obtained results confirm the efficiency of the GP algorithm for German and Australian datasets compared to other rule-based techniques to predict the credit risk.

Keywords: credit risk assessment, classification algorithms, data mining, rule extraction

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Authors: Hosein Rahmati

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The Fatimid government was one of the powerful Shiite governments that was formed in 297 AH in the Islamic Maghreb based on Ismaili ideas and played an important role in promoting the culture and civilization of the Islamic world. Ismaili is one of the Shiite sects that has its own beliefs and teachings. This research seeks to find out which of the Ismaili beliefs and teachings were considered by the Fatimid political government and which the Fatimid government paid serious attention to highlighting. The present study, based on library sources and descriptive-analytical method, has concluded that the Ismaili doctrinal foundations, especially the doctrine of Imamate, are essential elements in the formation and continuation of the Fatimid rule. Their goals were approaching.

Keywords: Fatimid rule, The Ismaili, The Islamic Maghreb, Imamate

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Authors: Iliya Musa Adamu

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This paper seeks to develop an expert system that would troubleshoot computer network and evaluate the network system performance so as to reduce the workload on technicians and increase the efficiency and effectiveness of solutions proffered to computer network problems. The platform of the system was developed using ASP.NET, whereas the codes are implemented in Visual Basic and integrated with SQL Server 2005. The knowledge base was represented using production rule, whereas the searching method that was used in developing the network troubleshooting expert system is the forward-chaining-rule-based-system. This software tool offers the advantage of providing an immediate solution to most computer network problems encountered by computer users.

Keywords: expert system, forward chaining rule based system, network, troubleshooting

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Authors: Rebeca Ramirez Acosta, Sebastian Lenhoff

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Decision makers worldwide need to determine if the implementation of a new market mechanism will contribute to the sustainability and resilience of the power system. Due to smart grid technologies, new products in the distribution and transmission system can be traded; however, the impact of changing a market rule will differ between several regions. To test systematically those impacts, a market categorization has been compiled and organized in a smart grid market testing toolbox. This toolbox maps all actual energy products and sets the basis for running a co-simulation test with the new rule to be implemented. It will help to measure the impact of the new rule, based on the sustainable and resilience indicators.

Keywords: co-simulation, electricity market, smart grid market, market testing

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Authors: Zhidong Zhang, Zhi-Chao Zhang

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This study investigated the structural validity of externalizing issues of Achenbach System of Empirically Based Assessment (ASEBA) via a Chinese sample. The externalizing problems consist of two sub-problems: rule-breaking behavior and aggressive behavior. The rule-breaking behavior consists of 17 items, and aggressive behavior consists of 18 items. The factor analysis model was used to examine the structure validity. For the rule breaking behavior, at the first step, the most items weighted with component 2. After the rotation, there was a clear weight on both component 1 and 2. For the aggressive behavior, at the first step, there was no clear picture about the components. After the rotation, two clusters of items were closer to component 1 and 2 respectively. It seemed that both rule breaking behavior issue and aggressive behavior issue suggested two components. Further studies should be done to examine both samples and structures of externalizing problems.

Keywords: confirmatory analysis, externalizing issue, structural validity, varimax rotations

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Authors: Ebrahim Taherzadeh, Helmi Z. M. Shafri, Kaveh Shahi

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One of the most important tasks in urban area remote sensing is detection of impervious surface (IS), such as building roof and roads. However, detection of IS in heterogeneous areas still remains as one of the most challenging works. In this study, detection of concrete roof using an object-oriented approach was proposed. A new rule-based classification was developed to detect concrete roof tile. The proposed rule-based classification was applied to WorldView-2 image. Results showed that the proposed rule has good potential to predict concrete roof material from WorldView-2 images with 85% accuracy.

Keywords: object-based, roof material, concrete tile, WorldView-2

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Authors: Wajdi Mohamed Ratemi

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The very well-known stacked sets of numbers referred to as Pascal’s triangle present the coefficients of the binomial expansion of the form (x+y)n. This paper presents an approach (the Staircase Horizontal Vertical, SHV-method) to the generalization of planar Pascal’s triangle for polynomial expansion of the form (x+y+z+w+r+⋯)n. The presented generalization of Pascal’s triangle is different from other generalizations of Pascal’s triangles given in the literature. The coefficients of the generalized Pascal’s triangles, presented in this work, are generated by inspection, using embedded Pascal’s triangles. The coefficients of I-variables expansion are generated by horizontally laying out the Pascal’s elements of (I-1) variables expansion, in a staircase manner, and multiplying them with the relevant columns of vertically laid out classical Pascal’s elements, hence avoiding factorial calculations for generating the coefficients of the polynomial expansion. Furthermore, the classical Pascal’s triangle has some pattern built into it regarding its odd and even numbers. Such pattern is known as the Sierpinski’s triangle. In this study, a presentation of Sierpinski-like patterns of the generalized Pascal’s triangles is given. Applications related to those coefficients of the binomial expansion (Pascal’s triangle), or polynomial expansion (generalized Pascal’s triangles) can be in areas of combinatorics, and probabilities.

Keywords: pascal’s triangle, generalized pascal’s triangle, polynomial expansion, sierpinski’s triangle, combinatorics, probabilities

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Authors: Triano Nurhikmat

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Along with the progress of science and technology, the development of the industrialized world in Indonesia took place very rapidly. This leads to a process of industrialization of society Indonesia faster with the establishment of the company and the workplace are diverse. Development of the industry relates to the activity of the worker. Where in these work activities do not cover the possibility of an impending crash on either the workers or on a construction project. The cause of the occurrence of industrial accidents was the fault of electrical damage, work procedures, and error technique. The method of an association rule is one of the main techniques in data mining and is the most common form used in finding the patterns of data collection. In this research would like to know how relations of the association between the incidence of any industrial accidents. Therefore, by using methods of analysis association rule patterns associated with combination obtained two iterations item set (2 large item set) when every factor of industrial accidents with a West Jakarta so industrial accidents caused by the occurrence of an electrical value damage = 0.2 support and confidence value = 1, and the reverse pattern with value = 0.2 support and confidence = 0.75.

Keywords: association rule, data mining, industrial accidents, rules

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Authors: Sangdeok Lee, Sangwon Han, Changtaek Hyun

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Construction defects are major components that result in negative impacts on project performance including schedule delays and cost overruns. Since construction defects generally occur when a few associated causes combine, a thorough understanding of defect causality is required in order to more systematically prevent construction defects. To address this issue, this paper uses association rule mining (ARM) to quantify the causality between defect causes, and social network analysis (SNA) to find indirect causality among them. The suggested approach is validated with 350 defect instances from concrete works in 32 projects in Korea. The results show that the interrelationships revealed by the approach reflect the characteristics of the concrete task and the important causes that should be prevented.

Keywords: causality, defect causes, social network analysis, association rule mining

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Authors: Tetsuro Saeki, Yuichi Kato, Shoutarou Mizuno

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STRIM (Statistical Test Rule Induction Method) has been proposed as a method to effectively induct if-then rules from the decision table which is considered as a sample set obtained from the population of interest. Its usefulness has been confirmed by simulation experiments specifying rules in advance, and by comparison with conventional methods. However, scope for future development remains before STRIM can be applied to the analysis of real-world data sets. The first requirement is to determine the size of the dataset needed for inducting true rules, since finding statistically significant rules is the core of the method. The second is to examine the capacity of rule induction from datasets with contaminated attribute values created by missing data and noise, since real-world datasets usually contain such contaminated data. This paper examines the first problem theoretically, in connection with the rule length. The second problem is then examined in a simulation experiment, utilizing the critical size of dataset derived from the first step. The experimental results show that STRIM is highly robust in the analysis of datasets with contaminated attribute values, and hence is applicable to realworld data.

Keywords: rule induction, decision table, missing data, noise

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Authors: Swapan Maiti, Dipanwita Roy Chowdhury

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Nonlinear functions are essential in different cryptoprimitives as they play an important role on the security of the cipher designs. Rule 30 was identified as a powerful nonlinear function for cryptographic applications. However, an attack (MS attack) was mounted against Rule 30 Cellular Automata (CA). Nonlinear rules as well as maximum period CA increase randomness property. In this work, nonlinear rules of maximum period nonlinear hybrid CA (M-NHCA) are studied and it is shown to be a better crypto-primitive than Rule 30 CA. It has also been analysed that the M-NHCA with single nonlinearity injection proposed in the literature is vulnerable against MS attack, whereas M-NHCA with multiple nonlinearity injections provide maximum length cycle as well as better cryptographic primitives and they are also secure against MS attack.

Keywords: cellular automata, maximum period nonlinear CA, Meier and Staffelbach attack, nonlinear functions

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Authors: Kate N. Okeke

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The ever-growing needs of man requiring satisfaction have pushed him strongly towards industrialization which has and is still leaving environmental degradation and its attendant negative impacts in its wake. It is, therefore, not surprising that the enjoyment of fundamental rights like food supply, security of lives and property, freedom of worship, health and education have been drastically affected by such degradation. In recognition of the imperative need to protect the environment and human rights, many global instruments and constitutions have recognized the right to a healthy and sustainable environment. Some environmental advocates and quite a number of literatures on the subject matter call for the recognition of environmental rights via rule of law as a vital means of achieving positive outcomes on the subject matter. However, although there are numerous countries with constitutional environmental provisions, most of them such as Nigeria, have shown poor environmental performance. A notable problem is the fact that the constitution which recognizes environmental rights appears in its other provisions to contradict its provisions by making enforceability of the environmental rights unattainable. While adopting a descriptive, analytical, comparative and explanatory study design in reviewing a successful positive environmental outcome via the rule of law, this article argues that rule of law on a balance of scale, weighs more than just environmental rights recognition and therefore should receive more attention by environmental lawyers and advocates. This is because with rule of law, members of a society are sure of getting the most out of the environmental rights existing in their legal system. Members of Niger-Delta communities of Nigeria will benefit from the environmental rights existing in Nigeria. They are exposed to environmental degradation and pollution with effects such as acidic rainfall, pollution of farmlands and clean water sources. These and many more are consequences of oil and gas exploration. It will also pave way for solving the violence between cattle herdsmen and farmers in the Middle Belt and other regions of Nigeria. Their clashes are over natural resource control. Having seen that environmental rule of law is vital to sustainable development, this paper aims to contribute to discussions on how best the vehicle of rule law can be driven towards achieving positive environmental outcomes. This will be in reliance on other enforceable provisions in the Nigerian Constitution. Other domesticated international instruments will also be considered to attain sustainable environment and development.

Keywords: environment, rule of law, constitution, sustainability

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Authors: Chinedu Peter, Dashrath Singh

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Membrane computing is a computability model which abstracts its structures and functions from the biological cell. The main ingredient of membrane computing is the notion of a membrane structure, which consists of several cell-like membranes recurrently placed inside a unique skin membrane. The emergence of several variants of membrane computing gives rise to the notion of a P system. The paper presents a variant of P systems for arithmetic operations on non-negative integers based on the weak priorities for rule application. Consequently, we obtain deterministic P systems. Two membranes suffice. There are at most four objects for multiplication and five objects for division throughout the computation processes. The model is simple and has a potential for possible extension to non-negative integers and real numbers in general.

Keywords: P system, binary operation, determinism, weak rule priority

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Authors: Fujio Takata

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When governments levy taxes on labor income on the basis of a balanced budget rule, two steady states in an economy exist, of which one can cause two movement patterns, namely, indeterminacy paths and a saddle path. However, in this paper, we assume an economy with divisible labor, in which labor adjustment is made by an intensive margin. We demonstrate that there indeed exist the two paths in the economy and that there exists a critical condition dividing them. This is proved by establishing the relationship between a finite elasticity of labor with regard to real wages and the share of capital in output. Consequently, we deduce the existence of an upper limit in the share of capital in output for indeterminacy to occur. The largest possible value of that share is less than 0.5698.

Keywords: balanced budget rule, divisible labor, labor income taxation, two movement patterns

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