Continuous Quantities Research Articles

Superior continuous quantity discrimination in a freshwater turtle

BackgroundQuantity discrimination, the ability to discriminate a magnitude of difference or discrete numerical information, plays a key role in animal behavior. While quantitative ability has been well documented in fishes, birds, mammals, and even in previously unstudied invertebrates and amphibians, it is still poorly understood in reptiles and has never been tested in an aquatic turtle despite the fact that evidence is accumulating that reptiles possess cognitive skills and learning ability. To help address this deficiency in reptiles, we investigated the quantitative ability of an Asian freshwater turtle, Mauremys sinensis, using red cubes on a white background in a trained quantity discrimination task. While spontaneous quantity discrimination methods are thought to be more ecologically relevant, training animals on a quantity discrimination task allows more comparability across taxa.ResultsWe assessed the turtles’ quantitative performance in a series of tests with increasing quantity ratios and numerosities. Surprisingly, the turtles were able to discriminate quantities of up to 9 versus 10 (ratio = 0.9), which shows a good quantitative ability that is comparable to some endotherms. Our results showed that the turtles’ quantitative performance followed Weber’s law, in which success rate decreased with increasing quantity ratio across a wide range of numerosities. Furthermore, the gradual improvement of their success rate across different experiments and phases suggested that the turtles possess learning ability.ConclusionsReptile quantitative ability has long been ignored and therefore is likely under-estimated. More comparative research on numerical cognition across a diversity of species will greatly contribute to a clearer understanding of quantitative ability in animals and whether it has evolved convergently in diverse taxa.

Optimization of the smart grids connected using an improved P&O MPPT algorithm and parallel active filters

This article presents a method for the reduction of harmonics generated by photovoltaic the smart grid connected. Photovoltaic generators always produce harmonics due to the nature of the direct current they generate. In order to eliminate these harmonics, parallel active filters are used. They are based on seven-level inverters. For the extraction of maximum power produced by the photovoltaic generators, the modified perturb and observe algorithm is used. Furthermore, to reduce the distortions due to the injected continuous quantities, the filtering of the harmonic quantities is done by four levels active filters using three switching cells per arm connected downstream of the seven-level inverters. The proposed algorithm and the model of active filter are evaluated, by calculating of the total harmonic distortion of the current after filtering. The rate of 0.21% is obtained. Additionally, the simulation results show this rate is lower than that of the standard Institute of Electrical and Electronics Engineers norms. Besides, the performance of the algorithm has been demonstrated when the solar panels are subjected to variations in irradiance.

Logic, geometry and visualisation of the body in Acquapendente’s rediscovered Methodus anatomica (1579)

AbstractThe article provides the first description and analysis of the recently rediscovered manuscript titled Methodus anatomica by Girolamo Fabrici da Acquapendente (1533–1619). Acquapendente was one of the most important anatomists in late sixteenth-century Europe and played an instrumental role as Harvey’s teacher in Padua towards the latter’s discovery of the circulation of the blood. The manuscript provides first-hand testimony as to how anatomy was administered in Padua in the post-Vesalian era and sheds light on a number of otherwise unknown aspects of the development of the anatomical method. Chiefly among these is the attention devoted by Acquapendente to historia, as a way to order sensory data in a consistent way, which draws widely from the geometrical method and from the contemporary debate on the discretisation of continuous quantities.

A classification-pursuing adaptive approach for Gaussian process regression on unlabeled data

Some areas of mechanical and system engineering such as dynamic systems commonly exhibit highly fluctuating responses over given parametric domains. Therefore, classifying some quantities of interest over the parametric domain for designing new systems turns out to be a highly challenging task. In this context, an innovative adaptive sampling algorithm named Monte Carlo-intersite Voronoi (MiVor) is proposed for design applications based on the classification of one or more continuous quantities of interest useful for parametric studies. In contrast to reliability analysis problems, no probabilistic setting and information is needed. The proposed technique is able to efficiently detect two or more classes of highly imbalanced decision regions and to accurately describe the boundary between these regions in a robust manner. To the best of the authors knowledge it is the first adaptive scheme for classification-pursuing parametric studies that combines information from (potentially) multiple class label outputs and the accompanying continuous values for efficient sampling involving (possibly) multiple class outputs. The resulting surrogates utilize only a small number of observations which are obtained in an active manner. The capabilities of the presented algorithm to provide accurate classification are demonstrated on three dynamic applications with various dimensionality and under consideration of a combination of different first-passage failure scenarios. Comparisons with two regression-based adaptive schemes show that the proposed algorithm outperforms existing methods. For instance, in the case of a quarter-car problem, more than 99% of points are correctly classified using the proposed approach at convergence, whereas less than 80% of reference samples are correctly classified with standard approaches. Similar performances (> 95%) are also obtained with MiVor for a non-linear oscillator of Duffing’s type and a three-degrees-of-freedom mass-spring system with three and six-dimensional parametric spaces respectively.

Spontaneous quantity discrimination in a family-living lizard

Abstract While foraging or during social interactions, animals may benefit from judging relative quantity. Individuals may select larger prey or a patch with more food and, likewise, it may pay to track the number and type of individuals and social interactions. We tested for spontaneous quantity discrimination in the gidgee skink (Egernia stokesii), a family-living lizard. Lizards were presented with food quantities differing in number or size and were able to select the larger quantity of food items when they differed in number but not when items differed in size. We show, for the first time, superior spontaneous discrimination of items differing in number over size in a lizard species, which contrasts with previous findings. Our simple method, however, did not include controls for the use of continuous quantities, and further tests are required to determine the role of such information during quantity discrimination. Our results provide support for the use of the parallel individuation system for the discrimination of small quantities (four or fewer items). Lizards might, however, still use the approximate number system if items in larger quantities (more than four) are presented. Overall, we uncovered evidence that species might possess specific cognitive abilities potentially adapted to their niche with respect to quantity information (discrete and/or continuous) and the processing system used when judging quantities. Importantly, our results highlight the need for testing multiple species using similar testing procedures to gain a better understanding of the underlying causes leading to differences across species.

Estimation of MCS intensity for Italy from high quality accelerometric data, using GMICEs and Gaussian Na\xefve Bayes Classifiers

Macroseismic intensity provides a qualitative description of seismic damage. It can be associated with Ground Motion Parameters (GMPs), which are extracted in near real-time from instrumental recordings during an earthquake. Several formulations of this empirical association exist in literature for Italy, mainly focusing on the relationship between intensity expressed on the Mercalli-Cancani-Sieberg (MCS) scale and peak ground acceleration or velocity. They are usually in the form of Ground Motion to Intensity Conversion Equations (GMICEs), which treat intensity as a continuous quantity. We propose an alternative approach, the Gaussian Naïve Bayes (GNB) classifiers, which allows to correctly treat intensity according to its ordinal definition. As a comparison, we also implement a modified version of the standard GMICE approach. We expand the existing database of GMP/MCS-intensity points with new, high-quality accelerometric data recorded in Italy in the period from 2002 to 2016 and resample the database by treating the intermediate intensities with half integer values (which are not meaningful in the MCS description) as both belong to the above and below full integer classes with an assigned weight. As a result, we estimate a new set of regression relations and GNB probability distributions between integer MCS intensity classes and eight GMPs (peak acceleration, velocity, displacement, Arias and Housner intensities, spectral acceleration at 0.3, 1.0 and 3.0 s). Results based on PGA and PGV are the most stable on the whole intensity scale. GNB models score better than GMICEs in terms of performance on unseen data and classification scores.

Continuous versus discrete quantity discrimination in dune snail (Mollusca: Gastropoda) seeking thermal refuges

The ability of invertebrates to discriminate quantities is poorly studied, and it is unknown whether other phyla possess the same richness and sophistication of quantification mechanisms observed in vertebrates. The dune snail, Theba pisana, occupies a harsh habitat characterised by sparse vegetation and diurnal soil temperatures well above the thermal tolerance of this species. To survive, a snail must locate and climb one of the rare tall herbs each dawn and spend the daytime hours in an elevated refuge position. Based on their ecology, we predicted that dune snails would prefer larger to smaller groups of refuges. We simulated shelter choice under controlled laboratory conditions. Snails’ acuity in discriminating quantity of shelters was comparable to that of mammals and birds, reaching the 4 versus 5 item discrimination, suggesting that natural selection could drive the evolution of advanced cognitive abilities even in small-brained animals if these functions have a high survival value. In a subsequent series of experiments, we investigated whether snails used numerical information or based their decisions upon continuous quantities, such as cumulative surface, density or convex hull, which co-varies with number. Though our results tend to underplay the role of these continuous cues, behavioural data alone are insufficient to determine if dune snails were using numerical information, leaving open the question of whether gastropod molluscans possess elementary abilities for numerical processing.

On the Sizing of the DC-Link Capacitor to Increase the Power Transfer in a Series-Series Inductive Resonant Wireless Charging Station

Wireless inductive-coupled power transfer is a very appealing technique for the battery recharge of autonomous devices like surveillance drones. The charger design mainly focuses on lightness and fast-charging to improve the drone mission times and reduce the no-flight gaps. The charger secondary circuit mounted on the drone generally consists of a full-bridge rectifier and a second-order filter. The filter cut-off frequency is usually chosen to make the rectifier output voltage constant and so that the battery is charged with continuous quantities. Previous works showed that an increase in power transfer is achieved, if compared to the traditional case, when the second-order filter resonant frequency is close to the double of the wireless charger excitation and the filter works in resonance. This work demonstrates that the condition of resonance is necessary but not sufficient to achieve the power increment. The bridge rectifier diodes must work in discontinuous-mode to improve the power transfer. The paper also investigates the dependence of the power transfer increase on the wireless excitation frequency. It is found the minimum frequency value below which the power transfer gain is not possible. This frequency transition point is calculated, and it is shown that the gain in power transfer is obtained for any battery when its equivalent circuit parameters are known. LTSpice simulations demonstrate that the transferred power can be incremented of around 30%, if compared to the case in which the rectifier works in continuous mode. This achievement is obtained by following the design recommendations proposed at the end of the paper, which trade off the gain in power transfer and the amplitude of the oscillating components of the wireless charger output.

Pertumbuhan Batang Bawah Karet pada Beberapa Komposisi Media Tanam dalam Root Trainer

The rubber tree rootstock nursery using the root trainer method is aimed to promote root growth through the use of non-soil growing media in a special container. This technology offers the advantages of a shortened breeding process, good rooting, and ease of delivery. The objective of this study is to investigate the effect of the planting media composition of oil palm bunches compost, manure, rice husk, solid decanter, and Trichoderma viride on the growth of rubber rootstock under the root trainer method. The research was carried out in the greenhouse of the Sungei Putih Research Center, Indonesian Rubber Research Institute, Deli Serdang, North Sumatra in January-May 2019. The observation included plant height, number of leaves, stem diameter, dry weight, and root length, and successful grafting percentage. The results indicated that the mixture of oil palm bunches compost, solid decanter, and Trichoderma viride (Te treatment) was the most potential to be developed as a planting media for rubber rootstock nursery under root trainer system. At 18 weeks after planting, the Te treatment had an average height of 82.66 + 14.27 cm with an increment rate of 3.25 + 0.81 cm/week, number of leaves 11.33 + 3.21 leaves with the increment of 0.52 + 0.20 leaves/week, stem diameter 5.29 + 0.73 mm with an increase of 0.33 + 0.05 mm/week. The Te treatment had a length and root weight of 41.97 + 2.40 cm and 1.68 + 0.77 g, respectively, with the grafting successfulness percentage of 47.37%. Besides showing good growth, these materials are also available in large and continuous quantities. The use of Trichoderma viride not only for increasing plant growth but also as a biocontrol of white root disease. Keywords: growth, growing media, Hevea brasiliensis, rootstock, root trainer

Early childhood mathematical development: the association between patterning and proportional reasoning

Insight into early precursors of proportional reasoning is necessary to further our theoretical understanding of mathematical development and to guide early interventions. Although several researchers have suggested patterning as a possible precursor for proportional reasoning, there is little empirical evidence to support this assumption, particularly at a young age. To address this gap, the current study explored if patterning in 4- to 5-year-olds (n = 346) is associated with proportional reasoning one and a half years later. Two measures of patterning ability (repeating and growing patterns) and two measures of proportional reasoning (one with discrete quantities and one with a discrete and a continuous quantity) were administered, together with measures addressing general cognitive and numerical abilities. Regression analyses showed that patterning is a unique predictor of proportional reasoning ability over and above sex and general cognitive and numerical abilities. An interaction effect between pattern types and the nature of the quantities was observed: Performance on repeating patterns was uniquely related to performance on proportional reasoning with two discrete quantities, whereas performance on growing patterns was uniquely related to performance on proportional reasoning with a discrete and a continuous quantity. Theoretical implications and suggestions for future studies are discussed.

The approximate number system represents magnitude and precision

Numbers are symbols manipulated in accord with the axioms of arithmetic. They sometimes represent discrete and continuous quantities (e.g., numerosities, durations, rates, distances, directions, and probabilities), but they are often simply names. Brains, including insect brains, represent the rational numbers with a fixed-point data type, consisting of a significand and an exponent, thereby conveying both magnitude and precision.

Development of methods for extension of the conceptual and analytical framework of the fuzzy set theory

Fuzzy set theory is an effective alternative to probability theory in solving many problems of studying processes and systems under conditions of uncertainty. The application of this theory is especially in demand in situations where the system under study operates under conditions of rapidly changing influencing parameters or characteristics of the environment. In these cases, the use of solutions obtained by standard methods of the probability theory is not quite correct. At the same time, the conceptual, methodological and hardware base of the alternative fuzzy set theory is not sufficiently developed. The paper attempts to fill existing gaps in the fuzzy set theory in some important areas. For continuous fuzzy quantities, the concept of distribution density of these quantities is introduced. Using this concept, a method for calculating the main numerical characteristics of fuzzy quantities, as well as a technology for calculating membership functions for fuzzy values of functions from these fuzzy quantities and their moments is proposed. The introduction of these formalisms significantly extends the capabilities of the fuzzy set theory for solving many real problems of computational mathematics. Using these formalisms, a large number of practical problems can be solved: fuzzy regression and clustering, fuzzy multivariate discriminant analysis, differentiation and integration of functions of fuzzy arguments, state diagnostics in a situation where the initial data are fuzzy, methods for solving problems of unconditional and conditional optimization, etc. The proof of the central limit theorem for the sum of a large number of fuzzy quantities is obtained. This proof is based on the characteristic functions of fuzzy quantities introduced in the work and described at the formal level. The concepts of independence and dependence for fuzzy quantities are introduced. The method for calculating the correlation coefficient for fuzzy numbers is proposed. Examples of problem solving are considered

Tracking computability of GPAC-generable functions

Abstract Analog computation attempts to capture any type of computation, that can be realized by any type of physical system or physical process, including but not limited to computation over continuous measurable quantities. A pioneering model is the General Purpose Analog Computer (GPAC), initially presented by Shannon in 1941. The GPAC is capable of manipulating real-valued data streams; however, it has been shown to be strictly less powerful than other models of computation on the reals, such as computable analysis. In previous work, we proposed an extension of the Shannon GPAC, denoted LGPAC, designed to overcome its limitations. Not only is the LGPAC model capable of expressing computation over general data spaces $\mathcal{X}$, but it also directly incorporates approximating computations by means of a limit module. An important feature of this work is the generalisation of the framework of the computation theory from Banach to Fréchet spaces. In this paper, we compare the LGPAC with a digital model of computation based on effective representations (tracking computability). We establish general conditions under which LGPAC-generable functions are tracking computable.

A sense of number in invertebrates

Non-symbolic numerical abilities are widespread among vertebrates due to their important adaptive value. Moreover, these abilities were considered peculiar of vertebrate species as numerical competence is regarded as cognitively sophisticated. However, recent evidence convincingly showed that this is not the case: invertebrates, with their limited number of neurons, proved able to successfully discriminate different quantities (e.g., of prey), to use the ordinal property of numbers, to solve arithmetic operations as addition and subtraction and even to master the concept of zero numerosity. To date, though, the debate is still open on the presence and the nature of a «sense of number» in invertebrates. Whether this is peculiar for discrete countable quantities (numerosities) or whether this is part of a more general magnitude system dealing with both discrete and continuous quantities, as hypothesized for humans and other vertebrates. Here we reviewed the main studies on numerical abilities of invertebrates, discussing in particular the recent findings supporting the hypothesis of a general mechanism that allows for processing of both discrete (i.e., number) and continuous dimensions (e.g., space).

Accuracy Increase of Discrete Sensors With Time Delay

The discrete sensors of continuous physical quantities are widely used in various technical systems. Real sensors have a considerable inertia and they operate in the conditions of random noises, therefore, they include the analog-to-digital interface. This interface creates discrete values of the input signal and suppresses the influence of random noises almost completely with application of the antialiasing filter. However, the discrete values are formed on the output of the analog-to-digital interface with some time delay. Therefore, the digital sensors have a large error, caused by this delay. In this article to eliminate this error an astatic high-speed discrete corrector is proposed. The error of the corrected discrete sensor is equal to zero at the steady-state mode, if the degree of the input polynomial signal is one unit less than the astatism order of the used corrector. It is supposed that the time delay of the discrete sensor is multiple to the sampling period of the analog-to-digital interface. To determine transfer functions of the discrete sensor and the astatic discrete corrector the formulas are obtained. The operation algorithm of the astatic high-speed discrete corrector is determined on the basis of its transfer function. The efficiency and feasibility with application of digital device of the proposed corrector is illustrated by the example of the sensor design with the astatism of the second order. The obtained results can be used in the development of highly precise discrete sensors of various physical quantities.

Calculus and counterpossibles in science

A mathematical model in science can be formulated as a counterfactual conditional, with the model’s assumptions in the antecedent and its predictions in the consequent. Interestingly, some of these models appear to have assumptions that are metaphysically impossible. Consider models in ecology that use differential equations to track the dynamics of some population of organisms. For the math to work, the model must assume that population size is a continuous quantity, despite that many organisms (e.g., rabbits) are necessarily discrete. This means our counterfactual representation of the model can have an impossible antecedent, giving us a counterpossible. Analogous counterpossibles arise in other sciences, as we’ll see. According to a prominent view in counterfactual semantics, the vacuity thesis, all counterpossibles are vacuously true, that is, true merely because their antecedents are necessarily false. But some counterpossible formulations of differential equation models in science are not all vacuously true—some are non-vacuously true, and some are false. I go on to show how an alternative semantics, one that employs impossible worlds, can deliver this judgment.

The impact of set size on cumulative area judgments

The ability to track number has long been considered more difficult than tracking continuous quantities. Evidence for this claim comes from work revealing that continuous properties (specifically cumulative area) influence numerical judgments, such that adults perform worse on numerical tasks when cumulative area is incongruent with number. If true, then continuous extent tracking abilities should be unimpeded by number. The aim of the present study was to determine the precision with which adults track cumulative area and to uncover the process by which they do so. Across two experiments, we presented adults with arrays of dots and asked them to judge the relative cumulative area of the displays. Participants performed worse and were slower on incongruent trials, in which the more numerous array had the smaller cumulative area. These findings suggest that number interferes with continuous quantity judgments, and that number is at least as salient as continuous variables, undermining claims in the literature that continuous properties are easier to represent, and more salient to adults. Our primary research question, however, pertained to how cumulative area representations were impacted by set size. Results revealed that the area of a single item was tracked much faster and with greater precision than the area of multiple items. However, for sets with more than one item, results revealed less accurate, yet faster responses, as set size increased, suggesting a speed-accuracy trade-off in judgments of cumulative area. Results are discussed in the context of two distinct theories regarding the process of tracking cumulative area.

Two‐agent scheduling with linear resource‐dependent processing times

AbstractThis paper considers a two‐agent scheduling problem with linear resource‐dependent processing times, in which each agent has a set of jobs that compete with that of the other agent for the use of a common processing machine, and each agent aims to minimize the weighted number of its tardy jobs. To meet the due date requirements of the jobs of the two agents, additional amounts of a common resource, which may be in discrete or continuous quantities, can be allocated to the processing of the jobs to compress their processing durations. The actual processing time of a job is a linear function of the amount of the resource allocated to it. The objective is to determine the optimal job sequence and resource allocation strategy so as to minimize the weighted number of tardy jobs of one agent, while keeping the weighted number of tardy jobs of the other agent, and the total resource consumption cost within their respective predetermined limits. It is shown that the problem is ‐hard in the ordinary sense, and there does not exist a polynomial‐time approximation algorithm with performance ratio unless ; however it admits a relaxed fully polynomial time approximation scheme. A proximal bundle algorithm based on Lagrangian relaxation is also presented to solve the problem approximately. To speed up convergence and produce sharp bounds, enhancement strategies including the design of a Tabu search algorithm and integration of a Lagrangian recovery heuristic into the algorithm are devised. Extensive numerical studies are conducted to assess the effectiveness and efficiency of the proposed algorithms.

Sweeping Area across Physical and Virtual Environments

The concept of area measure is widely viewed as fundamental. It is both intrinsically important and also structurally significant, as a representative of the class of continuous multiplicative quantities. Operating flexibly in this context with meaning and conceptual understanding is thus a critical objective for elementary education. Meanwhile, the difficulties learners encounter with area are well documented in the literature and include challenges with visualizing structured 2D space and conceptualizing the referent-transforming action that converts two length measures into area measure. Responding to these challenges, we present an analysis of their activity where third-grade learners generated figures with area by sweeping one length (a ‘squeegee’) through another length. We describe a ‘duo’ of physical and virtual learning environments that we developed to enable this ‘sweeping’ approach to area – and we show how this duo supported a classroom group of students in engaging with the two challenges mentioned above. In our analysis, we draw upon Charles Goodwin’s framework of co-operative action, showing how, at both individual and group levels, learners began to build professional vision around area measure and how the shared gestures they developed pointed toward emerging collective understanding of area as a dynamic quantity.

Effect Heterogeneity in Responding to Performance-Based Incentives: A Quasi-Experimental Comparison of Impacts on Health Service Indicators Between Hospitals and Health Centers in Malawi

ABSTRACT Heterogeneity of effects produced by performance-based incentives (PBIs) at different levels of care provision is not well understood. This study analyzes effect heterogeneities between different facility types resulting from a PBI program in Malawi. Identical PBIs were applied to both district hospitals and health centers to improve the performance of essential health services provision. We conducted two complementary quasi-experiments comparing all 17 interventions with 17 matched independent control facilities (each 12 health centers, five hospitals). A pre- and post-test design with difference-in-differences analysis was used to estimate effects on 14 binary quality indicators; interrupted time series analysis of monthly routine data was used to estimate effects on 11 continuous quantity indicators. Effects were estimated separately for health centers and hospitals. Most quality indicators performed high at baseline, producing ceiling effects on further measurable improvements. Significant positive effects were observed for stocks of iron supplements (hospitals) and partographs (health centers). Four quantity indicators showed similar positive trend improvements across facility types (first-trimester antenatal visits, voluntary HIV-testing of couples, iron supplementation in pregnancy, vitamin A supplementation of children); two showed no change for either type of facility (skilled birth attendance, fully immunized one-year-olds); five indicators revealed different effect patterns for health centers and hospitals. In both health centers and hospitals, the largely positive PBI effects on antenatal care included resilience against interrupted supply chains and improvements in attendance rates. Observed heterogeneity might have been influenced by the availability of specific resources or the redistribution of service use.