Formula Manipulation Research Articles

Impure Simplicial Complexes: Complete Axiomatization

Combinatorial topology is used in distributed computing to model concurrency and asynchrony. The basic structure in combinatorial topology is the simplicial complex, a collection of subsets called simplices of a set of vertices, closed under containment. Pure simplicial complexes describe message passing in asynchronous systems where all processes (agents) are alive, whereas impure simplicial complexes describe message passing in synchronous systems where processes may be dead (have crashed). Properties of impure simplicial complexes can be described in a three-valued multi-agent epistemic logic where the third value represents formulae that are undefined, e.g., the knowledge and local propositions of dead agents. In this work we present an axiomatization for the logic of the class of impure complexes and show soundness and completeness. The completeness proof involves the novel construction of the canonical simplicial model and requires a careful manipulation of undefined formulae.

PyKrev: A Python Library for the Analysis of Complex Mixture FT-MS Data.

In this paper, we present PyKrev, a Python library for the analysis of complex mixture Fourier transform mass spectrometry (FT-MS) data. PyKrev is a comprehensive suite of tools for analysis and visualization of FT-MS data after formula assignment has been performed. These comprise formula manipulation and calculation of chemical properties, intersection analysis between multiple lists of formulas, calculation of chemical diversity, assignment of compound classes to formulas, multivariate analysis, and a variety of visualization tools producing van Krevelen diagrams, class histograms, PCA score, and loading plots, biplots, scree plots, and UpSet plots. The library is showcased through analysis of hot water green tea extracts and Scotch whisky FT-ion cyclotron resonance-MS data sets. PyKrev addresses the lack of a single, cohesive toolset for researchers to perform FT-MS analysis in the Python programming environment encompassing the most recent data analysis techniques used in the field.

DEMOCRACIA ALGORITMICA:

Resumo: O uso de fórmulas algorítmicas para minerar dados extraídos das redes sociais, para elaborar perfis e induzir escolhas na política, além de resvalar na privacidade, reduz o debate de ideias que formam o pensamento livre, transformando as democracias em vultos espectrais. Esse cenário de disrupção, de hashtagzição da vida coletiva reduzindo o diálogo a rosnados coléricos e fake news, facilitou a desinformação e criou ambiente fértil para as milícias digitais, maquinaria da guerrilha política virtual para ganhar preferência dos eleitores indecisos. Indagando sobre o futuro da democracia nesses quadrantes, o presente artigo busca conceituar e caracterizar tais organizações, que desafiam o sistema de justiça analógico, desconectado da velocidade e estratégias dessa nova realidade. A abordagem do financiamento dessas organizações por grupos de empresários, além da irrigação de recursos públicos oriundos de gabinetes parlamentares, também oferece reflexões sobre o controle do abuso do poder político e econômico que impactam as eleições.

Predictive Control for Multi-Input Multi-Output System by Fast Distribution Based on Formula Manipulation

Predictive Control for Multi-Input Multi-Output System by Fast Distribution Based on Formula Manipulation

Development and accuracy evaluation of a degree of occlusion visualization system for roller pumps used in cardiopulmonary bypass.

In roller pumps used for cardiopulmonary bypass (CPB), the degree of blockage within the tube resulting from compression of the tube by the rollers, or the degree of occlusion, is closely related to hemolysis, with both tight occlusive and non-occlusive degrees promoting hemolysis. There are as yet no international standards regarding methods of adjusting occlusiveness, and the amount of mechanical stress exerted upon blood remains unknown. To prevent hemolysis during CPB using roller pumps, there is a need to clarify and quantitatively assess the mechanical stress of the occlusiveness of the roller pump. In this study, we have developed a degree of occlusion quantification system which constructs the flow channel shape within an occluded tube from red optical density images, and we have verified the validity of this system. Utilizing a linear actuator, an acrylic roller and raceway, a solution colored with simulated blood powder, and a 3/8-inch vinyl chloride tube, this system uses a camera to capture red optical density images within an occluded tube and constructs the tube flow channel shape using a formula manipulation system. To verify the accuracy of this system, we compared the thickness of a cross-section of the flow channel constructed with the degree of occlusion quantification system with the thickness of a cross-section of silicone cured under the same occlusion conditions. Our experiments indicated that for areas with a small tube gap, this system can construct highly accurate three-dimensional shapes and obtain quantitative indicators assessing the degree of occlusion.

Fast Model Predictive Control Based on Formula Manipulation and Finite Step Prediction

Fast Model Predictive Control Based on Formula Manipulation and Finite Step Prediction

The Evaluation of Computer Algebra Systems Using Fuzzy Multi-Criteria Decision-Making Models

The main purpose of this study is to present a systematic methodology based on fuzzy Multi-Criteria Decision-Making (FMCDM) models to help users evaluate computer algebra systems (CAS). CAS is a software package for the manipulation of mathematical formulas. The suggested methodology is user-centred which involves users' subjective evaluation judgments. User judgments are represented by means of fuzzy linguistic modelling techniques. An evaluation criteria framework based on the concept of the usefulness of CAS is developed. Next, two FMCDM models – fuzzy Analytical Hierarchy Process (FAHP) and fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) are proposed for the evaluation procedure. The FAHP is applied to determine the relative importance weights of qualitative evaluation criteria; the FTOPSIS is applied to rank the CAS alternatives. The illustrated case study demonstrates the applicability and effectiveness of the proposed methodology.

Exploring Edit Distance for Normalising Out-of-Vocabulary Malay Words on Social Media

Users interact using short-formed words and abbreviations and this results in a message full of noisy words that are not recognized by the system's knowledge. The aim of this research is to overcome the limitations that still bar the progression of normalizing Malay noisy words from social media platforms. The testing data gathered is 25,000; 15,000 Tweets from Twitter and 10,000 comments from Facebook respectively. Pre-processing steps were carried out to clean the entire dataset which consists of unique 179,786 words. 36,587 out-of-vocabulary (OOV) Malay terms were then extracted and checked against an in- vocabulary (IV) Malay corpus using the Levenshtein edit distance formula and character manipulation rules. The resultant output is 3,964 unique IV Malay words. Based on the results, the usage of edit distance and rules can be further improved to elevate the normalisation of the ever changing colloquial terms of the Malay language.

“The Etherealization of Common Sense?” Arithmetical and Algebraic Modes of Intelligibility in Late Victorian Mathematics of Measurement

The late nineteenth century gradually witnessed a liberalization of the kinds of mathematical object and forms of mathematical reasoning permissible in physical argumentation. The construction of theories of units illustrates the slow and difficult spread of new “algebraic” modes of mathematical intelligibility, developed by leading mathematicians from the 1830s onwards, into elementary arithmetical pedagogy, experimental physics, and fields of physical practice like telegraphic engineering. A watershed event in this process was a clash that took place during 1878 between J. D. Everett and James Thomson over the meaning and algebraic manipulation of dimensional formulae. This precipitated the emergence of rival “Maxwellian” and “Thomsonian” approaches towards interpreting and applying “dimensional” equations, which expressed the relationship between derived and fundamental units in an absolute system of measurement. What at first looks like a dispute over a seemingly esoteric mathematical tool for unit conversion turns out to concern Everett’s break with arithmetical algebra in the representation and manipulation of physical quantities. This move prompted a vigorous rebuttal from Thomsonian defenders of an orthodox “arithmetical empiricism” on epistemological, semantic, or pedagogical grounds. Their resistance in Victorian Britain to a shift in mathematical intelligibility is suggestive of the difficult birth of theoretical physics, in which the intermediate steps of a mathematical argument need have no direct physical meaning.

Extension of Optimization Problems under Supply and Demand Balance by Introducing Weighting Factors and Its Fast Solution Based on Formula Manipulation

Extension of Optimization Problems under Supply and Demand Balance by Introducing Weighting Factors and Its Fast Solution Based on Formula Manipulation

A Knowledge Level Account of Forgetting

Forgetting is an operation on knowledge bases that has been addressed in different areas of Knowledge Representation and with respect to different formalisms, including classical propositional and first-order logic, modal logics, logic programming, and description logics. Definitions of forgetting have been expressed in terms of manipulation of formulas, sets of postulates, isomorphisms between models, bisimulations, second-order quantification, elementary equivalence, and others. In this paper, forgetting is regarded as an abstract belief change operator, independent of the underlying logic. The central thesis is that forgetting amounts to a reduction in the language, specifically the signature, of a logic. The main definition is simple: the result of forgetting a portion of a signature in a theory is given by the set of logical consequences of this theory over the reduced language. This definition offers several advantages. Foremost, it provides a uniform approach to forgetting, with a definition that is applicable to any logic with a well-defined consequence relation. Hence it generalises a disparate set of logic-specific definitions with a general, high-level definition. Results obtained in this approach are thus applicable to all subsumed formal systems, and many results are obtained much more straightforwardly. This view also leads to insights with respect to specific logics: for example, forgetting in first-order logic is somewhat different from the accepted approach. Moreover, the approach clarifies the relation between forgetting and related operations, including belief contraction.

最適性条件と数式処理による省エネルギーのための高速最適分配制御

Energy management systems (EMSs) have been widely developed for efficient energy usage. Optimization of operation of energy consuming plants is one of key technologies in EMS. In this paper, we propose a very fast optimization method for optimal load distribution problems by which we can implement optimizing functions on microcomputers without high speed CPU or rich RAM. The proposing method consists of two phases, offline formula manipulation phase and online fast calculation phase. We show that the proposing method can give a strict optimal solution without any violation of constraints within 96 times shorter time than a traditional gradient method. The proposing method can contribute low cost and ubiquitous optimization for EMS.

Extended drill‐down operator: Digging into the structure of performance indicators

SummaryPerformance measurement is the subject of interdisciplinary research on information systems, organizational modeling and decision support systems. The data cube model is usually adopted to represent performance indicators (PI) and enable flexible analysis, visualization and reporting. However, the major obstacles against effective design and management of PI monitoring systems are related to the facts that PIs are complex objects with an aggregate/compound nature. This often leads to unawareness of indicator semantics as well as of dependencies among indicators. In this work, we propose to enrich the data cube model with the formal description of the structure of an indicator given in terms of its algebraic formula and aggregation function. Such a model enables the definition of a novel operator, namely indicator drill‐down, which relies on formula manipulation functionalities and reasoning. Like the usual drill‐down, this operator increases the detail of a measure of the data cube by expanding an indicator into its components. Thus, the two notions of drill‐down are integrated, allowing a novel way of data exploration. As a proof‐of‐concept, an implementation of the approach is presented. The evaluation of the implementation on real and synthetic scenarios enlightens the effectiveness and the efficiency of the approach. Copyright © 2015 John Wiley & Sons, Ltd.

HyLaGI: Symbolic Implementation of a Hybrid Constraint Language HydLa

A modeling language for hybrid systems HydLa and its implementation HyLaGI are described. HydLa is a constraint-based language that can handle uncertainties of models smoothly. HyLaGI calculates trajectories by symbolic formula manipulation to exclude errors resulting from floating-point arithmetic. HyLaGI features a nondeterministic simulation algorithm so it can calculate all possible qualitative different trajectories of models with uncertainties.

On Product Distance of Lattice Code over a Biquadratic Number Field

Lattice code is a type of error correcting codes composed of the image of embedding map of an integral ideal in a certain algebraic number field with a bilinear form. In a mobile communication, transmitted signals are attenuated by phenomenon called fading, and the Rayleigh fading of multi-path radio wave is one of important and essential type of fading. Some lattice codes are applicable in order to mitigate the influence of the fading and to extract the most feasible source information from the received signal. The minimum product distance is one of key indicators of lattice code along with the modulation diversity. In this paper, we show some experimental results on the minimum product distance for some lattices of prime ideal in a composition fields of two real quadratic fields using a free formula manipulation system, PARI/GP.

Counting and generating lambda terms

AbstractLambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation. This paper tries to answer questions like: How many terms of a given size are there? What is a ‘typical’ structure of a simply typable term? Despite their ostensible simplicity, these questions still remain unanswered, whereas solutions to such problems are essential for testing compilers and optimizing programs whose expected efficiency depends on the size of terms. Our approach toward the aforementioned problems may be later extended to any language with bound variables, i.e., with scopes and declarations. This paper presents two complementary approaches: one, theoretical, uses complex analysis and generating functions, the other, experimental, is based on a generator of lambda terms. Thanks to de Bruijn indices (de Bruijn, N. (1972) Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem. Indagat. Math.34(5), 381–392), we provide three families of formulas for the number of closed lambda terms of a given size and we give four relations between these numbers which have interesting combinatorial interpretations. As a by-product of the counting formulas, we design an algorithm for generating λ-terms. Performed tests provide us with experimental data, like the average depth of bound variables and the average number of head lambdas. We also create random generators for various sorts of terms. Thereafter, we conduct experiments that answer questions like: What is the ratio of simply typable terms among all terms? (Very small!) How are simply typable lambda terms distributed among all lambda terms? (A typable term almost always starts with an abstraction.) In this paper, abstractions and applications have size 1 and variables have size 0.

On delay-dependent stability conditions for Takagi–Sugeno fuzzy systems

This paper presents new less conservative stability analysis conditions for Takagi–Sugeno fuzzy systems subject to interval time-varying delay. The methodology is based on the direct Lyapunov method allied with an appropriate Lyapunov–Krasovskii functional choice and the use of the integral inequalities, Finsler lemma, Newton–Leibniz formula manipulations and convex combination properties. Particularly, the main result differs from previous ones since the positiveness of the Lyapunov–Krasovskii functional is guaranteed by new relaxed conditions. Two examples illustrate the effectiveness of the proposed methodology.

Uma trajetória dos profissionais de saúde ingleses, 1815-1858

The article recounts the process of regulating the health professions in England from 1815 to 1858. Impelled by the period's epidemics, this was also the time of the sanitary reform, in which health professionals devoted themselves to aiding the ill. Since the technical attributions of each type of professional were not clearly defined, this field of un-regulated practices became divided into two areas: the provision of medical advice and the manipulation of formulas. Three important measures changed the field of medical and pharmacological practices: the Apothecaries Act (1815), the Pharmacy Act (1852), and the Medical Act (1858). These laws were a mixed reflection of the interests of the State, medical professionals, and British society.

An Improved Algorithm for Network Reliability Evaluation

Binary Decision Diagram (BDD) is a data structure proved to be compact in representation and efficient in manipulation of Boolean formulas. Using Binary decision diagram in network reliability analysis has already been investigated by some researchers. In this paper, we show how an exact algorithm for network reliability can be improved and implemented efficiently by using a Colorado University Decision Diagram (CUDD).

114 ボールキック運動における逆-順動力学解析環境の構築(サッカーキックほか)

In studies dealing with body movement and sports techniques, a method that is commonly used involves analysing joint torque using inverse dynamics based on kinematic data obtained through motion capture systems. On the other hand, another analytic technique that has become increasingly common entails generating movements and performing simulations on the basis of the force data for joint torque and the like; this technique employs forward dynamics to calculate the kinematic data. In general, however, the inverse dynamics and forward dynamics analyses are performed independently, and there have been almost no studies in which analysis is conducted by combining the two analyses. Therefore, in this study, an analytic environment was constructed for analysing the motion of kicking a soccer ball, in which inverse dynamics and forward dynamics were combined; the environment was constructed by using a formula manipulation language based on a simple two-dimensional double pendulum model. The results showed that although the kinematic data obtained from the motion capture system did not completely match the kinematic data obtained from the simulation in which forward dynamics was used, adequate agreement was observed between the two sets of data. In this study, it was considered that the development of an analytic environment that combined inverse dynamics and forward dynamics enabled a more refined analysis of the motion of kicking a ball.