Dhavit Prem, Fernando Sotomayor, Alvaro Saldívar
et al.
Yupana is an Inca device used for arithmetic operations. This article describes a new arithmetical system: Tawa Pukllay (TP), where arithmetic operations do not require mental calculations: no carries, no borrows, no memorization of multiplication tables, nor trial and error procedures for divisions. Instead, user recognizes patterns and makes predefined movements to perform the four basic arithmetic operations very quickly; moreover, the result of the operation can be reached by multiple paths and in parallel, allowing each user to create his own strategies. This paper proves with mathematical rigor that TP produces correct numerical results.
SynDiffix is a new open-source tool for structured data synthesis. It has anonymization features that allow it to generate multiple synthetic tables while maintaining strong anonymity. Compared to the more common single-table approach, multi-table leads to more accurate data, since only the features of interest for a given analysis need be synthesized. This paper compares SynDiffix with 15 other commercial and academic synthetic data techniques using the SDNIST analysis framework, modified by us to accommodate multi-table synthetic data. The results show that SynDiffix is many times more accurate than other approaches for low-dimension tables, but somewhat worse than the best single-table techniques for high-dimension tables.
Robert A. M. Basili, Wenyang Qian, Shiplu Sarker
et al.
The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor's algorithm, weighted sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM's superconducting qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands' superposed integer states. We analyze performance, and identify the most effective approximation depths for unsigned quantum addition and quantum multiplication within the given context. We then perform a similar analysis of signed addition and compare to the unsigned results. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges - relevant to signed, unsigned, modular and non-modular versions - that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. We analyze the performance trends in our results and speculate on possible future developments within this computational paradigm.
Sourav Chowdhury, Sourabh Kumar Manna, Suparna Roychowdhury
et al.
Here, we develop a mathematical model for glucose-insulin regulatory system. The model includes a new parameter which is the amount of ingested glucose. Ingested glucose is an external glucose source coming from digested food. We assume that the external glucose or ingested glucose decays exponentially with time. We establish a system of three linear ordinary differential equations with this new parameter, derive stability analysis and the solution of this model.
Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and strategies. Mathematics can also be applied to the entire making of music, from the score to the performance, connecting compositional structures to acoustical reality of sounds. Moreover, the precise concept of gesture has a decisive role in understanding musical performance. In this paper, we apply some concepts of category theory to compare gestures of orchestral musicians, and to investigate the relationship between orchestra and conductor, as well as between listeners and conductor/orchestra. To this aim, we will introduce the concept of gestural similarity. The mathematical tools used can be applied to gesture classification, and to interdisciplinary comparisons between music and visual arts.
Research Computing demands are exploding beyond traditional disciplines due to the proliferation of data in all walks of life. At Bentley University ("Bentley"), a business university in the Boston area, this expansion has been most readily seen in our Accounting, Economics, Mathematics, and Natural Sciences departments. The result has been a small effort to build a research computing capability at this small New England university. This poster will serve as an overview of the steps taken to build such an effort at a business university, the revelations we have had along the way, and our plans for the future.
Identifying the quality factor of JPEG images is very useful for applications in digital image forensics. Though several command-line tools exist and are used in widely used software such as \emph{GIMP} (GNU Image Manipulation Program), the well-known image editing software, or the \emph{ImageMagick} suite, we have found that those may provide inaccurate or even wrong results. This paper presents a simple method for determining the exact quality factor of a JPEG image from its quantization tables. The method is presented briefly and a sample program, written in Unix/Linux Shell bash language is provided.
We analyse two classes of $(1+2)$ evolution equations which are of special interest in Financial Mathematics, namely the Two-dimensional Black-Scholes Equation and the equation for the Two-factor Commodities Problem. Our approach is that of Lie Symmetry Analysis. We study these equations for the case in which they are autonomous and for the case in which the parameters of the equations are unspecified functions of time. For the autonomous Black-Scholes Equation we find that the symmetry is maximal and so the equation is reducible to the $(1+2)$ Classical Heat Equation. This is not the case for the nonautonomous equation for which the number of symmetries is submaximal. In the case of the two-factor equation the number of symmetries is submaximal in both autonomous and nonautonomous cases. When the solution symmetries are used to reduce each equation to a $(1+1)$ equation, the resulting equation is of maximal symmetry and so equivalent to the $(1+1)$ Classical Heat Equation.
The most popular approach for solving fully fuzzy linear programming (FFLP) problems is to convert them into the corresponding deterministic linear programs. Khan et al. (2013) [Khan, I. U., Ahmad, T., & Maan, N. (2013). A simplified novel technique for solving fully fuzzy linear programming problems. Journal of Optimization Theory and Applications, 159(2), 536-546.] claimed that there had been no method in the literature to find the fuzzy optimal solution of a FFLP problem without converting it into crisp linear programming problem, and proposed a technique for the same. Others showed that the fuzzy arithmetic operation used by Khan et al. (2013) had some problems in subtraction and division operations, which could lead to misleading results. Recently, Ezzati et al. (2014) [Ezzati, R., Khorram, E., & Enayati, R. (2014). A particular simplex algorithm to solve fuzzy lexicographic multi-objective linear programming problems and their sensitivity analysis on the priority of the fuzzy objective functions. Journal of Intelligent and Fuzzy Systems, 26(5), 2333-2358.] defined a new operation on symmetric trapezoidal fuzzy numbers and proposed a new algorithm to find directly a lexicographic/preemptive fuzzy optimal solution of a fuzzy lexicographic multi-objective linear programming problem by using new fuzzy arithmetic operations, but their model was not fully fuzzy optimization. In this paper, a new method, by using Ezzati et al. (2014)’s fuzzy arithmetic operation and a fuzzy version of simplex algorithm, is proposed for solving FFLP problem whose parameters are represented by symmetric trapezoidal fuzzy number without converting the given problem into crisp equivalent problem. By using the proposed method, the fuzzy optimal solution of FFLP problem can be easily obtained. A numerical example is provided to illustrate the proposed method.
Analysis, Business mathematics. Commercial arithmetic. Including tables, etc.
In the past, different methods for asset depreciation have been defined but most of these procedures deal with certain parameters and inputs. The availability of certain parameters in many real world situations is difficult and sometimes impossible. The primary objective of this paper is to obtain methods for calculating depreciation where some of the defined parameters are under uncertainty. Hence, by using the fuzzy science basics, extension principle and α-cut technique, we rewrite some classic methods for calculating depreciation in fuzzy form. Then, for comparing the methods of fuzzy depreciation under uncertain conditions by using the formula of calculating the Fuzzy Present worth (FPW), the Present worth of Tax saving (PWTS) of any aforementioned methods has been obtained. Finally, since the amount of tax savings achieved for each of the methods is a fuzzy number, one of the fuzzy prioritization methods is used in order to select the best depreciation technique.
Analysis, Business mathematics. Commercial arithmetic. Including tables, etc.
Paul Brillant Feuto Njonko, Sylviane Cardey, Peter Greenfield
et al.
Business rules represent the primary means by which companies define their business, perform their actions in order to reach their objectives. Thus, they need to be expressed unambiguously to avoid inconsistencies between business stakeholders and formally in order to be machine-processed. A promising solution is the use of a controlled natural language (CNL) which is a good mediator between natural and formal languages. This paper presents RuleCNL, which is a CNL for defining business rules. Its core feature is the alignment of the business rule definition with the business vocabulary which ensures traceability and consistency with the business domain. The RuleCNL tool provides editors that assist end-users in the writing process and automatic mappings into the Semantics of Business Vocabulary and Business Rules (SBVR) standard. SBVR is grounded in first order logic and includes constructs called semantic formulations that structure the meaning of rules.
Marjan Naderinejad, Mohammad Jafar Tarokh, Alireza Poorebrahimi
Business Intelligence, not as a tool of a product but as a new approach is propounded in organizations to make tough decisions in business as shortly as possible. Hospital managers often need business intelligence in their fiscal, operational, and clinical reports and indices. The main goal of recognition and ranking CSF is implementation of a business intelligent system in hospitals to increase success factor of application of business intelligence in health and treatment sector. This paper is an application and descriptive-analytical one, in which we use questionnaires to gather data and we used SPSS and LISREL to analyze them. Its statistical society is managers and personnel of Hasheminejad hospital and case studies are selected by Cochran formula. The findings show that all three organizational, process, and technological factors equally affect implementation of business intelligence based on Yeoh & Koronis approach, where the assumptions are based upon it. The proposed model for CSFs of business intelligence in hospitals include: declaring perspective, goals and strategies, development of human and financial resources, clarification of organizational culture, documentation and process mature, management support, etc. Business intelligence implementation is affected by different components. Center of Hasheminejad hospital BI system as a leader in providing quality health care, partially succeeded to take advantage of the benefits the organization in passing the information revolution but the development of this system to achieve intelligent hospital and its certainty is a high priority, thus it can`t be said that the hospital-wide BI system is quite favorable. In this regard, it can be concluded that Hasheminejad hospital requires practical model for business intelligence systems development.
Being an emerging business practice, gamification is going to the mainstream to enable and transform social business initiatives across enterprises. With the consistent focus on customer behavior and experience, there is a paradigm shift in thinking about how Gamification and Social initiatives together help to increase the engagement level of knowledge worker, yielding better business results. Business scenarios for gamification are wide spread ranging from customer service and support to communities and collaboration. The Paper discusses the characteristics & mechanism to learn from games that are important for businesses to understand and apply. It also gives insights on gamification trends, real-world business challenges and also describes on how game thinking can revolutionize the business and create an engaging experience.
Nowadays social media (Twitter, Facebook, etc.), not only simply as communication media, but also for promotion. Social networking media offers many business benefits for companies and organizations. Research purposes is to determine the model of social network media utilization as a promotional media for handicraft business in Palembang city. Qualitative and quantitative research design are used to know how handicraft business in Palembang city utilizing social media networking as a promotional media. The research results show 35% craft businesses already utilizing social media as a promotional media. The social media used are blog development 15%, facebook 46%, and twitter etc. are 39%. The reasons they use social media such as, 1) minimal cost, 2) easily recognizable, 3) global distribution areas. Social media emphasis on direct engagement with customers better. So that the marketing method could be more personal through direct communication with customers.
Throughout the course of mathematical history, generalizations of previously understood concepts and structures have led to the fruitful development of the hierarchy of number systems, non-euclidean geometry, and many other epochal phases in mathematical progress. In the study of formalized theories of arithmetic, it is only natural to consider the extension from the standard model of Peano arithmetic, $\langle \mathbb{N},+,\times,\leq,0,1 \rangle$, to non-standard models of arithmetic. The existence of non-standard models of Peano arithmetic provided motivation in the early $20^{th}$ century for a variety of questions in model theory regarding the classification of models up to isomorphism and the properties that non-standard models of Peano arithmetic have. This paper presents these questions and the necessary results to prove Tennenbaum's Theorem, which draws an explicit line between the properties of standard and non-standard models; namely, that no countable non-standard model of Peano arithmetic is recursive. These model-theoretic results have contributed to the foundational framework within which research programs developed by Skolem, Rosser, Tarski, Mostowski and others have flourished. While such foundational topics were crucial to active fields of research during the middle of the $20^{th}$ century, numerous open questions about models of arithmetic, and model theory in general, still remain pertinent to the realm of $21^{st}$ century mathematical discourse.
The World Wide Web is a popular and interactive medium to distribute information in this scenario. The web is huge, diverse, ever changing, widely disseminated global information service center. We are familiar with terms like e-commerce, e-governance, e-market, e-finance, e-learning, e-banking etc. for an organization it is new challenge to maintain direct contact with customers because of the rapid growth in e-commerce, e-publishing and electronic service delivery. To deal with this there is need of intelligent marketing strategies and CRM (customer relationship management) i.e. the effective way of integrating enterprise applications in real time. Web mining is the vast field that helps to understand various concepts of different fields. Web usage mining techniques are attempted to reason about different materialized issues of Business Intelligence which include marketing expertise as domain knowledge and are specifically designed for electronic commerce purposes. To this end, the chapter provides an introduction to the field of Web mining and examines existing as well as potential Web mining applications applicable for different business function, like marketing, human resources, and fiscal administration. Suggestions for improving information technology infrastructure are made, which can help businesses interested in Web mining hit the ground running.
Het begrip economische waarde wordt vaak gebruikt maar ook slecht begrepen. De verwarring met het begrip prijs lijkt vrijwel onuitroeibaar. De subjectivistische (marginalistische) revolutie van 1871 levert een solide fundament voor een consistente waardeleer. In het dagelijks leven valt echter waar te nemen dat de mainstream opvattingen leiden tot een objectivistische benadering van het economisch waardebegrip. Daardoor verdwijnt de essentie en worden onjuiste conclusies getrokken. In dit artikel staat het waardebegrip uit de Oostenrijkse School centraal. Omdat mensen slechts kunnen handelen met het oog op de toekomst kan economische waarde alleen worden bepaald door, ex ante, uit te gaan van de positie en situatie van partijen.
Business, Business mathematics. Commercial arithmetic. Including tables, etc.
In dit artikel wordt onderzoek verricht naar een belangrijk aspect van de kwaliteit van halfjaarcijfers van beursgenoteerde ondernemingen in Nederland, de transparantie van de winst. Wij onderzoeken in hoeverre het management van beursgenoteerde ondernemingen in Nederland meer discretie over de financiële verslaggeving uitoefent bij het opstellen van halfjaarcijfers dan bij het opstellen van jaarcijfers. De onderzoeksresultaten tonen dat de transparantie van de winst in halfjaarberichten niet overeenkomt met de transparantie van de winst in de jaarrekening voor de jaren 1998 tot en met 2008. De implementatie van de Transparantierichtlijn per 1 januari 2009 kan, door verplichte naleving van IAS 34 bij het opstellen van de halfjaarcijfers, het verschil in de transparantie van de winst doen afnemen.
Business, Business mathematics. Commercial arithmetic. Including tables, etc.
In this paper we study the computation of Markov bases for contingency tables whose cell entries have an upper bound. In general a Markov basis for unbounded contingency table under a certain model differs from a Markov basis for bounded tables. Rapallo, (2007) applied Lawrence lifting to compute a Markov basis for contingency tables whose cell entries are bounded. However, in the process, one has to compute the universal Gröbner basis of the ideal associated with the design matrix for a model which is, in general, larger than any reduced Gröbner basis. Thus, this is also infeasible in small- and medium-sized problems. In this paper we focus on bounded two-way contingency tables under independence model and show that if these bounds on cells are positive, i.e., they are not structural zeros, the set of basic moves of all $2 \times 2$ minors connects all tables with given margins. We end this paper with an open problem that if we know the given margins are positive, we want to find the necessary and sufficient condition on the set of structural zeros so that the set of basic moves of all $2 \times 2$ minors connects all incomplete contingency tables with given margins.