Continuous Quantities Research Articles

Continuity, limits, and quantity in Al-Fārābī’s paraphrase of Aristotle’s Categories

ABSTRACT Despite its position in an introductory work to logic, the account of continuity presented by Abū Naṣr Al-Fārābī in his paraphrase of Aristotle’s Categories is apparently even less accessible to the beginner than Aristotle’s original. This is in part because Al-Fārābī integrated elements of the accounts of continuity in Aristotle’s Physics and Metaphysics into an account mainly derived from Aristotle’s Categories. While Al-Fārābī’s account chiefly follows Aristotle’s Categories 6 in describing a continuous object that can be divided into parts with a shared boundary, it borrows the terminology of limits from Physics 5 and the notion of quantity as divisible into its parts from Metaphysics 5.13. In doing so, Al-Fārābī defines continuity using a notion of a limit without determining whether or not it was part of the continuous quantity. This definition could also accommodate atomists, since it would work even if the limit were an atom or several atoms that were part of the continuous object. The broadness of this definition is probably intended to allow students of logic who may have atomist tendencies to accept the account of quantity in the categories tradition, even though they may not be ready to reject atomism until after studying physics.

의미론적 정합성 관점에서 분수의 연산 단원 분석: 의미 관계와 수량 유형을 중심으로

Mathematical concepts are derived from real-world situations, and their construction and application can be facilitated when real-world meanings and mathematical meanings are aligned. According to educational psychology research, the depth of interpretation and use of operations depend on whether the semantic relations between the objects presented in the problem situation and the potential mathematical relations are consistent. This study analyzed the semantic relations between objects in problem situations and the semantic alignment between the quantity types of objects and visual models in the fraction operation units of elementary school mathematics textbooks. The analysis revealed that, in problem situations, symmetric relationships were predominantly presented in fraction addition, subset-set relationships in fraction subtraction, and asymmetric relationships in fraction multiplication and division. Regarding quantity types, continuous quantities were presented more often than discrete ones, and in most cases, the quantity type of the object matched that of the visual model, though a few did not. Based on these findings, implications were drawn for selecting problem situations and instructional models that align with mathematical meanings and support student understanding from the perspective of mathematics learning psychology.

The Fourier–Malliavin Volatility (FMVol) MATLAB® library

This paper presents the Fourier–Malliavin Volatility (FMVol) estimation library for MATLAB®. This library includes functions that implement Fourier–Malliavin estimators (see Malliavin and Mancino (2002, 2009)) of the volatility and co-volatility of continuous stochastic volatility processes and second-order quantities, like the quarticity (the squared volatility), the volatility of volatility and the leverage (the covariance between changes in the process and changes in its volatility). The Fourier–Malliavin method is fully non-parametric, does not require equally-spaced observations and is robust to measurement errors, or noise, without any preliminary bias correction or pre-treatment of the observations. Furthermore, in its multivariate version, it is intrinsically robust to irregular and asynchronous sampling. Although originally introduced for a specific application in financial econometrics, namely the estimation of asset volatilities, the Fourier–Malliavin method is a general method that can be applied whenever one is interested in reconstructing the latent volatility and second-order quantities of a continuous stochastic volatility process from discrete observations.

Building a More Robust Introduction to Measurement in Research Method Courses

AbstractMeasurement is integral to science. Given that it takes many years to become knowledgeable in measurement, it is valuable to consider current practices in teaching measurement to undergraduate psychology students. It is argued here that psychology research method courses could benefit from significant additions and clarifications in the topic of measurement. Three topics to consider are: discussions of different measurement viewpoints, the conditions for continuous quantities, and measurement challenges in psychology. These topics can be integrated into our courses and would translate to a more nuanced understanding of measurement and a greater ability to critically think about measurement in psychology. Suggested strategies for teaching about these topics are also discussed.

Multidimensional Multi-Connected Fuzzy Interval-Logic Controller

The key features and the principle of operation of a multidimensional fuzzy interval-logic controller with interconnected adjustable parameters developed by the authors are considered. The scheme of interpretation of continuous physical quantities by an equivalent set of terms and the basic version of the block diagram of the regulator are presented. The main elements of the logical output block are described, including the block of production rules, which includes a predefined database of values of control actions on control objects in the form of ordinal numbers of terms of output continuous quantities. The advantages and features of setting up the mutual connections between the input and output continuous values of the regulator are considered, which is expressed in determining the functional dependencies between them. The set of parameters possessed by the terms of input continuous quantities in relation to specific output continuous quantities of the regulator is described. The methods of defuzzification of the values of output continuous quantities within the boundaries of their terms are shown. The possibility of combining input and output continuous quantities into groups when setting up mutual connections between them is described. The mechanism of determining groups of interrelated continuous quantities is illustrated, the total number of which is determined by forming a matrix of relationships, according to the author’s scheme. The algorithm of sequential processing of the contents of the cells of the matrix of relationships, consisting of three steps, is considered. Expressions are given for calculating the basic parameters of a multidimensional fuzzy interval-logic controller with interrelated adjustable parameters. The results of a computational experiment to reduce the system of production rules of the regulator in determining the relationships between input and output continuous quantities are presented.

Perceptual addition of continuous magnitudes in an ‘artificial algebra’

Although there is substantial evidence for an innate ‘number sense’ that scaffolds learning about mathematics, whether the underlying representations are based on discrete or continuous perceptual magnitudes has been controversial. Yet the nature of the computations supported by these representations has been neglected in this debate. While basic computation of discrete non-symbolic quantities has been reliably demonstrated in adults, infants, and non-humans, far less consideration has been given to the capacity for computation of continuous perceptual magnitudes. Here we used a novel experimental task to ask if humans can learn to add non-symbolic, continuous magnitudes in accord with the properties of an algebraic group, by feedback and without explicit instruction. Three pairs of experiments tested perceptual addition under the group properties of commutativity (Experiments 1a-b), identity and inverses (Experiments 2a-b) and associativity (Experiments 3a-b), with both line length and brightness modalities. Transfer designs were used in which participants responded on trials with feedback based on sums of magnitudes and later were tested with novel stimulus configurations. In all experiments, correlations of average responses with magnitude sums were high on trials with feedback. Responding on transfer trials was accurate and provided strong support for addition under all of the group axioms with line length, and for all except associativity with brightness. Our results confirm that adult human subjects can implicitly add continuous quantities in a manner consistent with symbolic addition over the integers, and that an ‘artificial algebra’ task can be used to study implicit computation.

Assessing Statistical Indices for Calibrating Building Performance Simulation Models via Continuous Time Series

In engineering planning practice, building simulation is becoming increasingly crucial for evaluating buildings’ energetic and thermal behaviour. The appropriate application in the form of models that represent reality precisely, therefore, faces the challenge of realistic parameter specification for uncertain BES model properties. Many of them can only be restricted to a probable range of values. Additional knowledge can be obtained for the case of available measurement data via inverse modelling. This approach minimises cost function values representing discrepancies between associated time series (measured and simulated data sets). Much research has been published in this field for energy consumption characteristics. These approaches differ in several aspects from measured continuous physical state quantities. This article applies general cost indices to air temperature measurement series. For isolated effects such as time delay and amplitude attenuation, the impact on the characteristic values is examined, and their response is evaluated. This survey leads to the conclusion that there is no single parameter suitable for identifying all effects, and a combination is recommended. A new proposal is made for such a combined statistical index, and exemplary applied for measured temperature curves from a castle near Potsdam.

Multiple model estimation under perspective of random-fuzzy dual interpretation of unknown uncertainty

This study considered the problem of multiple model estimation from the perspective of sigma-max inference (probability - possibility inference), while focusing on discovering whether certain of the unknown quantities involved could be more faithfully modeled as fuzzy uncertainty. Two related key issues were addressed: 1) The random-fuzzy dual interpretation of unknown quantity being inferred. 2) The principle of selecting sigma-max operator for estimation and recognition. This study considered that any continuous unknown quantity involved in estimation should be more appropriately modeled as randomness and handled by sigma inference; whereas, a discrete unknown quantity involved in recognition could be better modeled as fuzziness and handled by max inference. Consequently, the interacting multiple model (IMM) filter was reformulated in the framework of sigma-max inference, where the Markovian jump system was reformulated as a hybrid uncertainty system, with continuous state evolution modeled as usual as model-conditioned stochastic systems and discrete mode transition modeled as a fuzzy system using a possibility transition matrix, and hypotheses mixing was conducted by using the operation of “max” instead of “sigma.” For our examples of time series prediction and maneuvering target tracking, the updated IMM filter exhibited remarkable improvement over the classic IMM filter.

A REVIEW ON BEYOND HORMONE REPLACEMENT THERAPY (HRT): AYURVEDIC MANAGEMENT OF PERIMENOPAUSE.

According to WHO statistics, 467 million women were projected to be in perimenopause state in the year 1990, and this number is expected to increase to 1200 million by 2030. It is defined as the transitional period of two to eight years, antecedent to menopause and one year following the last menstrual period when the endocrinological and biological changes occur. In today’s scenario, women have a multifaceted perspective and contribute to society by their preposterous physical and mental achievements in every domain. The menopausal transition is amalgamated by different vasomotor, mental, genital, locomotor and GIT-related manifestations and consequently requires treatment for the same. In Ayurvedic texts, perimenopause can be compared with Rajonivritti janya kaal. When estrogen production falls below a critical value, it no longer impedes the production of FSH and LH; instead, they are produced in large and continuous quantities around menopause, but as the remaining primordial follicles become atretic, the production of estrogen by the ovaries falls eventually. The following physiological changes are noticed due to the loss of estrogen in the female body: Hot flushes characterized by extreme flushing of the skin, psychic sensation of dyspnea, irritability, fatigue, anxiety, decreased strength and calcification of bones throughout the body. There is a need for multi-centred randomized trials and future research in this domain where the fundamentals of Ayurveda can be incorporated into menopause management.

(Invited) Effect of Gaseous Tritium Environments on Betavoltaic Device Longevity

Direct betavoltaic energy conversion is a specialized energy harvesting technology, converting beta radiation from a radiation source directly into electricity using a semiconductor. Of the most common beta emitting isotopes, tritium betavoltaics hold promise owing to the high specific activity of solid tritium compounds, low shielding requirements and relatively high availability. Betavoltaic devices offer great promise to produce continuous quantities of nanowatt to microwatt power over the course of several years, particularly for low-power sensor, medical, and space applications where sunlight is too sparse for solar cell use or where battery replacement is challenging.Canadian Nuclear Laboratories (CNL) is currently developing betavoltaic devices based on tritium. CNL has unique facilities to produce, fabricate and test betavoltaic devices. Computational techniques have been used to address challenges of longevity and electron-hole pair generation in semiconductor materials, in particular (In,Ga)P. Long-term studies on test wafers in different tritium-containing environments and the effects on power output and longevity will also be discussed.

Accurate and Wide-Voltage-Range Modeling of Electrowetting with a Lattice Boltzmann Approach.

The lattice Boltzmann method (LBM) has been widely used in multi-phase fluid mechanics and is known to be more computationally efficient than the traditional method of numerically solving Navier-Stokes and Cahn-Hilliard equations. Electrowetting is an important component of interfacial sciences, in which the liquid-liquid and solid-liquid interfaces are tuned by electrostatics. Modeling electrowetting using the LBM can be categorized into surface and bulk methods. By modifying the surface tension scalar, the surface method easily reproduces the fundamental Young-Lippmann (YL) equation at low voltages but fails to capture contact angle saturation at high voltages. With fully coupled hydrodynamics and electrostatics in the form of spatially dependent matrices, the bulk method can successfully show contact angle saturation, but it is often unable to reproduce the YL equation due to its intrinsic inaccuracies. The inaccuracies are mainly due to the fact that while the hydrodynamics are all described by continuous physical quantities in the framework of diffusive interfaces, the interfacial electrostatics are governed by discontinuous electric fields caused by sheet charge density. In this paper, we show that accurately modeling electrowetting using the LBM is non-trivial. Additional modeling work, especially the treatment of interfacial electric fields, is needed to recover the fundamental YL equation at low voltages and predict contact angle saturation at high voltages, with a systematic model validation over key parameters and applications.

Controlling the physical field using the shape function technique

Abstract A field is described as a region under the influence of some physical force, such as electricity, magnetism, or heat. It is a continuous distribution in the space of continuous quantities. The characteristics of the field are that the values vary continuously between neighboring points. However, because of the continuous nature of the field, it is possible to approximate a physical field of interpolation operations to reduce the cost of sampling and simplify the calculation. This article introduces the modeling of the parametric intensity of physical fields in a general form based on the interpolation shape function technique. Besides the node points with sample data, there are interpolation points, whose accuracy depends significantly on the type of interpolation function and the number of node points sampled. Therefore, a comparative analysis of theoretical shape functions (TSFs) and experimental shape functions (ESFs) is carried out to choose a more suitable type of shape function when interpolating. Specifically, the temperature field is the quantity selected to apply, analyze, and conduct experiments. Theoretical computations, experiments, and comparisons of results have been obtained for each type of shape function in the same physical model under the same experimental conditions. The results show that ESF has an accuracy (error of 0.66%) much better than TSF (error of 10.34%). Moreover, the field model surveyed by a generalized reduced gradient algorithm allows for identifying points with the required parameter values presented in detail. The illustrated calculations on temperature field control in the article show that the solution for both forward and reverse problems can be determined very quickly with high accuracy and stability. Therefore, this technique is expected to be entirely feasible when applied to thermal control processes such as drying in paint technology, kilns, and heat dissipation in practice.

Multi-region dynamic economic dispatch with active power real-time balance constraint

In this paper, a multi-region dynamic economic dispatch model with power balance constraint is constructed to seek the actual reserve demand and reasonable reserve allocation method of the system by relying on the dynamic response process of the units to the power balance of the interconnected system. For this kind of dynamic optimization problem with differential equation constraints, a discrete-optimization rolling solution strategy based on scale-optimization is proposed. First, in the discrete part of the dispatching model, basing on the correlation between the continuous quantities discrete scale and the active real-time balancing effect of the dispatching scheme, a continuous quantities discrete scale optimization strategy is proposed to maintain the safe and economic operation of the system; then, for the convergence problem of the solution of the dispatching model after discretization, this paper introduces the idea of decentralized coordination optimization and the operator splitting quadratic programming (OSQP), and through the limited information exchange between the regional grid and the coordinator, the consistent coordination of consistent variables is achieved. The simulation results verify the effectiveness of the model and the solution strategy.

A stochastic game framework for patrolling a border

In this paper we consider a stochastic game for modelling the interactions between smugglers and a patroller along a border. The problem we examine involves a group of cooperating smugglers making regular attempts to bring small amounts of illicit goods across a border. A single patroller has the goal of preventing the smugglers from doing so, but must pay a cost to travel from one location to another. We model the problem as a two-player stochastic game and look to find a Nash equilibrium to gain insight into real world problems. Our framework extends the literature by assuming that the smugglers choose a continuous quantity of contraband, complicating the analysis of the game. We discuss a number of properties of Nash equilibria, including the aggregation of smugglers, the discount factors of the players, and the equivalence of our non zero-sum game to a zero-sum game. Additionally, we present algorithms to find Nash equilibria that are more computationally efficient than existing methods. We also consider certain assumptions on the parameters of the model that give interesting equilibrium strategies for the players.

Introducing in China the Aristotelian Category of Quantity: From the Coimbra Commentary on the Dialectics (1606) to the Chinese Mingli tan (1636-­1639)

Second Scholasticism greatly developed the medieval theory of continuous quantity as the Aristotelian notion for thematizing spatial extension, paving the way for the idea of space as extension in early modern natural philosophy. The article analyzes the section related to the category of continuous quantity in the Coimbra commentary on the Dialectics (1606), showing that it is indebted to the novel theory of Francisco Suárez on quantity as bestowing extension to a body in a particular sense, something which had been overlooked by previous research. The scholarly debate on quantity was brought to China, and here the Chinese translation is examined of the section on quantity in the fourth volume of the Mingli Tan, published in China in 1636-­1639.

Influence of measurement uncertainty on machine learning results demonstrated for a smart gas sensor

Abstract. Humans spend most of their lives indoors, so indoor air quality (IAQ) plays a key role in human health. Thus, human health is seriously threatened by indoor air pollution, which leads to 3.8 ×106 deaths annually, according to the World Health Organization (WHO). With the ongoing improvement in life quality, IAQ monitoring has become an important concern for researchers. However, in machine learning (ML), measurement uncertainty, which is critical in hazardous gas detection, is usually only estimated using cross-validation and is not directly addressed, and this will be the main focus of this paper. Gas concentration can be determined by using gas sensors in temperature-cycled operation (TCO) and ML on the measured logarithmic resistance of the sensor. This contribution focuses on formaldehyde as one of the most relevant carcinogenic gases indoors and on the sum of volatile organic compounds (VOCs), i.e., acetone, ethanol, formaldehyde, and toluene, measured in the data set as an indicator for IAQ. As gas concentrations are continuous quantities, regression must be used. Thus, a previously published uncertainty-aware automated ML toolbox (UA-AMLT) for classification is extended for regression by introducing an uncertainty-aware partial least squares regression (PLSR) algorithm. The uncertainty propagation of the UA-AMLT is based on the principles described in the Guide to the Expression of Uncertainty in Measurement (GUM) and its supplements. Two different use cases are considered for investigating the influence on ML results in this contribution, namely model training with raw data and with data that are manipulated by adding artificially generated white Gaussian or uniform noise to simulate increased data uncertainty, respectively. One of the benefits of this approach is to obtain a better understanding of where the overall system should be improved. This can be achieved by either improving the trained ML model or using a sensor with higher precision. Finally, an increase in robustness against random noise by training a model with noisy data is demonstrated.

A new discrete dynamical friction estimator based on N-body simulations

ABSTRACT A long-standing problem in galactic simulations is to resolve the dynamical friction (DF) force acting on massive black hole particles when their masses are comparable to or less than the background simulation particles. Many sub-grid models based on the traditional Chandrasekhar DF formula have been proposed, yet they suffer from fundamental ambiguities in the definition of some terms in Chandrasekhar’s formula when applied to real galaxies, as well as difficulty in evaluating continuous quantities from (spatially) discrete simulation data. In this work, we present a new sub-grid DF estimator based on the discrete nature of N-body simulations, which also avoids the ambiguously defined quantities in Chandrasekhar’s formula. We test our estimator in the gizmo code and find that it agrees well with high-resolution simulations where DF is fully captured, with negligible additional computational cost. We also compare it with a Chandrasekhar estimator and discuss its applications in real galactic simulations.

Effects of prefrontal and parietal neuromodulation on magnitude processing and integration.

Numerical cognition is an essential skill for survival, which includes the processing of discrete and continuous quantities, involving a mainly right fronto-parietal network. However, the neurocognitive systems underlying the processing and integration of discrete and continuous quantities are currently under debate. Noninvasive brain stimulation techniques have been used in the study of the neural basis of numerical cognition with a spatial, temporal and functional resolution superior to other neuroimaging techniques. The present randomized sham-controlled single-blinded trial addresses the involvement of the right dorsolateral prefrontal cortex and the right intraparietal sulcus in magnitude processing and integration. Multifocal anodal transcranial direct current stimulation was applied online during the execution of magnitude comparison tasks in three conditions: right prefrontal, right parietal and sham stimulation. The results show that prefrontal stimulation produced a moderated decrease in response times in all magnitude processing and integration tasks compared to sham condition. While parietal stimulation had no significant effect on any of the tasks. The effect found is interpreted as a generalized improvement in processing speed and magnitude integration due to right prefrontal neuromodulation, which may be attributable to domain-general or domain-specific factors.

Dealing with counts and other quantal quantities in quantity calculus

Continuity is usually assumed as a defining feature of measured quantities. This premise is false for counted quantities, amount of substance, electric charge, and others that are constrained to exist in integral multiples of a quantum. A software application that treats these quantities as continuous can predict outcomes that are physically impossible, such as the production of half a photon. Thus far, formalizations of quantity calculus have not addressed how quantities that are structured like the integers should interoperate with continuous quantities. This article introduces the extension of quantity calculus to include quantal quantities, which vary in steps rather than continuously, and discusses the consequences of including them.

Continuous Quantity and Quality Modeling for Assessing the Effect of SUDS: Application on a Conceptual Urban Drainage Basin

The development of computational tools based on urban drainage models is fundamental for the correct selection of SUDS. The present study proposes a systematic approach based on continuous modeling on USEPA SWMM. The objective was to select the most suitable Sustainable Urban Drainage Systems (SUDS) by evaluating several aspects related to their design and configuration. The proposed methodology was applied to a conceptual watershed with meteorological information from Santander, Spain. The analysis of SUDS design parameters showed that only the surface variables showed a sensitivity of ≈20% for berm height and vegetation volume. The optimal configuration for the case study was a SUDS train consisting of green roofs, permeable pavements, vegetated swales and rain gardens, with 1% of the total subcatchment area cover, one structure, and a semi-aggregated spatial distribution. The methodology proved efficient but also highly dependent on the case study parameters and the meteorological conditions. The SUDS proved to have different efficiencies (30%—90%) in reducing the total runoff volume, the peak flow, and the pollutant loads depending on the region where the conceptual watershed was modeled. The methodology proved to be efficient for studying the combinations and interconnection of seven different typologies, as well as the effect of SUDS configuration, design and distribution on their performance.