scholarly journals Backward transfer influences from quadratic functions instruction on students’ prior ways of covariational reasoning about linear functions

2021 ◽  
Vol 61 ◽  
pp. 100834
Author(s):  
Charles Hohensee ◽  
Sara Gartland ◽  
Laura Willoughby ◽  
Matthew Melville
Keyword(s):  
Linear Functions ◽  
Quadratic Functions ◽  
Covariational Reasoning

scholarly journals Effects of transient temperature on human's heat losses

2016 ◽  
Vol 20 (3) ◽  
pp. 827-830
Author(s):  
Lijuan Wang ◽  
Yuhui Di ◽  
Hui Yin ◽  
Yanfeng Liu ◽  
Jiaping Liu
Keyword(s):  
Energy Balance ◽  
Air Conditioning ◽  
Heat Losses ◽  
Linear Functions ◽  
Quadratic Functions ◽  
Balance Model ◽  
Transient Temperature ◽  
Convection Diffusion ◽  
Comfort Evaluation ◽  
And Diffusion

The objectives of the paper are to analyze human convection, radiation, evaporation, respiration, conduction, and diffusion heat losses when the operative temperature increases from 26-34.4?C and then decreases from 34.4-26?C with a ratio of 1.4?C per 5 minutes. A energy balance model is used for sedentary subject. The results show that during temperature rising, all the heat losses are linear functions of temperature, while during temperature dropping, the convection, diffusion, and respiration heat losses are quadratic functions of temperature. The results are useful for thermal comfort evaluation and heating, ventilation, and air conditioning design.

scholarly journals Controlled Functional Encryption Revisited: Multi-Authority Extensions and Efficient Schemes for Quadratic Functions

2021 ◽  
Vol 2021 (1) ◽  
pp. 21-42
Author(s):  
Miguel Ambrona ◽  
Dario Fiore ◽  
Claudio Soriente
Keyword(s):  
Homomorphic Encryption ◽  
Linear Functions ◽  
Quadratic Functions ◽  
Functional Encryption ◽  
Fine Grained ◽  
Multiple Data ◽  
Garbled Circuits ◽  
Private Data ◽  
Data Owner ◽  
Single Data

AbstractIn a Functional Encryption scheme (FE), a trusted authority enables designated parties to compute specific functions over encrypted data. As such, FE promises to break the tension between industrial interest in the potential of data mining and user concerns around the use of private data. FE allows the authority to decide who can compute and what can be computed, but it does not allow the authority to control which ciphertexts can be mined. This issue was recently addressed by Naveed et al., that introduced so-called Controlled Functional encryption (or C-FE), a cryptographic framework that extends FE and allows the authority to exert fine-grained control on the ciphertexts being mined. In this work we extend C-FE in several directions. First, we distribute the role of (and the trust in) the authority across several parties by defining multi-authority C-FE (or mCFE). Next, we provide an efficient instantiation that enables computation of quadratic functions on inputs provided by multiple data-owners, whereas previous work only provides an instantiation for linear functions over data supplied by a single data-owner and resorts to garbled circuits for more complex functions. Our scheme leverages CCA2 encryption and linearly-homomorphic encryption. We also implement a prototype and use it to showcase the potential of our instantiation.

scholarly journals Credibility Approximations for Bayesian Prediction of Second Moments

1985 ◽  
Vol 15 (2) ◽  
pp. 103-121 ◽  
Author(s):  
William S. Jewell ◽  
Rene Schnieper
Keyword(s):  
Least Squares ◽  
Linear Functions ◽  
Quadratic Functions ◽  
Sample Variance ◽  
Credibility Theory ◽  
Sample Mean ◽  
Second Moment ◽  
Second Moments ◽  
Special Cases ◽  
The Mean

AbstractCredibility theory refers to the use of linear least-squares theory to approximate the Bayesian forecast of the mean of a future observation; families are known where the credibility formula is exact Bayesian. Second-moment forecasts are also of interest, for example, in assessing the precision of the mean estimate. For some of these same families, the second-moment forecast is exact in linear and quadratic functions of the sample mean. On the other hand, for the normal distribution with normal-gamma prior on the mean and variance, the exact forecast of the variance is a linear function of the sample variance and the squared deviation of the sample mean from the prior mean. Bühlmann has given a credibility approximation to the variance in terms of the sample mean and sample variance.In this paper, we present a unified approach to estimating both first and second moments of future observations using linear functions of the sample mean and two sample second moments; the resulting least-squares analysis requires the solution of a 3 × 3 linear system, using 11 prior moments from the collective and giving joint predictions of all moments of interest. Previously developed special cases follow immediately. For many analytic models of interest, 3-dimensional joint prediction is significantly better than independent forecasts using the “natural” statistics for each moment when the number of samples is small. However, the expected squared-errors of the forecasts become comparable as the sample size increases.

Prediction of vernalisation in three Australian Vrn responsive wheats

2003 ◽  
Vol 54 (3) ◽  
pp. 283 ◽  
Author(s):  
L. D. J. Penrose ◽  
H. M. Rawson ◽  
M. Zajac
Keyword(s):  
Quadratic Function ◽  
Linear Interpolation ◽  
Development Stage ◽  
Linear Functions ◽  
Quadratic Functions ◽  
Published Data ◽  
Floral Initiation ◽  
Maximum Temperatures ◽  
Double Ridge ◽  
Interpolation Functions

This study sought to better estimate vernalisation in winter wheats, so that their early development and time of anthesis can be better predicted. For this, an accurate relationship between temperature and the effectiveness of vernalisation is required. Using previously published data, our study found that the relationship between temperature and effectiveness of vernalisation can be suitably described by a quadratic function. In contrast, most previous studies used linear interpolation functions to describe vernalising effectiveness. These consist of a series of linear functions of temperature over adjoining temperature ranges. An advantage of quadratic functions is that they allow effectiveness of vernalisation to be described in terms of underlying physiological processes, and require the estimation of fewer parameters to predict wheat development. Our study found the cardinal temperatures for vernalisation to be –3�C, 6.5�C, and 15.9�C, that is for the lower, optimum, and maximum temperatures respectively. To allow for different upper temperature limits for vernalisation, 2 quadratic temperature-vernalising effectiveness functions were used to predict accumulated daily vernalisation at 3 field sites. These predictions of daily vernalisation were compared with corresponding estimates produced with 3 previously proposed linear interpolation functions. Varying degrees of agreement were found between estimates produced by the 2 types of vernalising effectiveness functions. Equations that have been developed to predict floral initiation in winter wheats have not been previously evaluated in Australian field environments. These equations utilise the same underlying relationship between accumulated daily vernalisation and a measure of floral initiation, often the appearance of double ridges. Two of these equations were used to predict the appearance of double ridges for a field-grown Australian winter wheat, JF87%014. Neither equation could satisfactorily predict the timing of the double ridge development stage for this wheat, whatever vernalising effectiveness function was used to predict vernalisation in the field. Both equations had greatest difficulty in predicting the double ridge stage, in environments where vernalisation most delayed development. This finding suggests that equations currently predicting floral initiation in winter wheats do not utilise an accurate relationship between accumulated vernalisation and floral initiation. An alternative method of predicting anthesis in winter wheats is to predict final leaf number, but this approach has not been reliably applied in environments where vernalising temperatures vary.

scholarly journals Eggplant growth as affected by bovine manure and magnesium thermophosphate rates

2008 ◽  
Vol 65 (1) ◽  
pp. 77-86 ◽  
Author(s):  
Marinice Oliveira Cardoso ◽  
Walter Esfrain Pereira ◽  
Ademar Pereira de Oliveira ◽  
Adailson Pereira de Souza
Keyword(s):  
Leaf Area ◽  
Dry Matter ◽  
Quadratic Function ◽  
Potassium Sulfate ◽  
Linear Functions ◽  
Quadratic Functions ◽  
Positive Interaction ◽  
Relative Growth ◽  
High K ◽  
Cow Urine

Plant growth is influenced by nutrient availability. The objective of this research was to study, under greenhouse conditions, eggplant growth as affected by rates of bovine manure and magnesium thermophosphate (g kg-1 and mg kg-1, respectively), according to a "Box central composite" matrix: 4.15-259; 4.15-1509; 24.15-259; 24.15-1509; 0.0-884; 28.3-884; 14.15-0,0; 14.15-1768; 14.15-884. Potassium sulfate (170 mg kg-1) and 200 mL per pot of cow urine solution were applied four times, but the concentration of the last two applications (200 mL/H2O L) was twice of that of the first two. Additional treatments: magnesium thermophosphate without cow urine and triple superphosphate with urea, both with nutrient levels equivalent to the bovine manure, P2O5 and potassium sulfate to the combination 14.15-884. The experimental design consisted of randomized blocks with four replicates. Leaf area (LA) and LA ratio increased as quadratic functions with manure rates, with negative interaction for thermophosphate. Leaf dry matter mass (DMM) had an increasing quadratic function with rates for both fertilizers. The higher combined rates of both fertilizers resulted in the smallest specific leaf area, but also the highest values of shoot and root DMM, total DMM and, with positive interaction in relation to root shoot dry matter ratio. The relative growth rate in stem height, and also in diameter, increased with manure, according to quadratic and linear functions, respectively. The cow urine effect was, in general, lower than that of urea. The plant's overall growth was more influenced by manure. Root DMM and shoot DMM were greater with high K and P.

Extrapolating body masses in large terrestrial vertebrates

Paleobiology ◽  
2017 ◽  
Vol 43 (4) ◽  
pp. 693-699 ◽  
Author(s):  
Nicolás E. Campione
Keyword(s):  
Body Mass ◽  
Model Fitting ◽  
The Body ◽  
Linear Functions ◽  
Quadratic Functions ◽  
Quadratic Model ◽  
Implicit Assumption ◽  
Terrestrial Vertebrates ◽  
Scaling Models ◽  
Degree Term

AbstractDespite more than a century of interest, body-mass estimation in the fossil record remains contentious, particularly when estimating the body mass of taxa outside the size scope of living animals. One estimation approach uses humeral and femoral (stylopodial) circumferences collected from extant (living) terrestrial vertebrates to infer the body masses of extinct tetrapods through scaling models. When applied to very large extinct taxa, extant-based scaling approaches incur obvious methodological extrapolations leading some to suggest that they may overestimate the body masses of large terrestrial vertebrates. Here, I test the implicit assumption of such assertions: that a quadratic model provides a better fit to the combined humeral and femoral circumferences-to-body mass relationship. I then examine the extrapolation potential of these models through a series of subsetting exercises in which lower body-mass sets are used to estimate larger sets. Model fitting recovered greater support for the original linear model, and a nonsignificant second-degree term indicates that the quadratic relationship is statistically linear. Nevertheless, some statistical support was obtained for the quadratic model, and application of the quadratic model to a series of dinosaurs provides lower mass estimates at larger sizes that are more consistent with recent estimates using a minimum convex-hull (MCH) approach. Given this consistency, a quadratic model may be preferred at this time. Still, caution is advised; extrapolations of quadratic functions are unpredictable compared with linear functions. Further research testing the MCH approach (e.g., the use of a universal upscaling factor) may shed light on the linear versus quadratic nature of the relationship between the combined femoral and humeral circumferences and body mass.

Clustering in the presence of side information: a non-linear approach

2019 ◽  
Vol 12 (2) ◽  
pp. 292-314
Author(s):  
Ahmad Ali Abin
Keyword(s):  
Linear Method ◽  
Quadratic Function ◽  
Background Knowledge ◽  
Kernel Functions ◽  
Linear Functions ◽  
Quadratic Functions ◽  
Target Space ◽  
Constrained Clustering ◽  
Content Type ◽  
Non Linear

Purpose Constrained clustering is an important recent development in clustering literature. The goal of an algorithm in constrained clustering research is to improve the quality of clustering by making use of background knowledge. The purpose of this paper is to suggest a new perspective for constrained clustering, by finding an effective transformation of data into target space on the reference of background knowledge given in the form of pairwise must- and cannot-link constraints. Design/methodology/approach Most of existing methods in constrained clustering are limited to learn a distance metric or kernel matrix from the background knowledge while looking for transformation of data in target space. Unlike previous efforts, the author presents a non-linear method for constraint clustering, whose basic idea is to use different non-linear functions for each dimension in target space. Findings The outcome of the paper is a novel non-linear method for constrained clustering which uses different non-linear functions for each dimension in target space. The proposed method for a particular case is formulated and explained for quadratic functions. To reduce the number of optimization parameters, the proposed method is modified to relax the quadratic function and approximate it by a factorized version that is easier to solve. Experimental results on synthetic and real-world data demonstrate the efficacy of the proposed method. Originality/value This study proposes a new direction to the problem of constrained clustering by learning a non-linear transformation of data into target space without using kernel functions. This work will assist researchers to start development of new methods based on the proposed framework which will potentially provide them with new research topics.

Effect of Temperature on Time from Planting to Flowering in Virginia Type Peanuts (Arachis hypogaea L.)1

1974 ◽  
Vol 1 (2) ◽  
pp. 86-90 ◽  
Author(s):  
F. R. Cox ◽  
C. K. Martin
Keyword(s):  
Empirical Relation ◽  
Mathematical Expression ◽  
Field Studies ◽  
Linear Functions ◽  
Quadratic Functions ◽  
Effect Of Temperature ◽  
Maximum Temperature ◽  
Daily Maximum ◽  
Heat Unit ◽  
The Individual

Abstract Field studies with a planting date variable were utilized to determine an empirical relation between time from planting to first flowering of NC2, NC5, and Florigiant peanuts and minimum and maximum daily temperatures. Two basic types of curvilinear response functions and two heat unit systems, which used linear functions, were compared on the basis of days missed by each prediction. The mathematical expression of the data that gave the least days missed was the daily fraction of time to flowering being the sum of quadratic functions for minimum and maximum temperature. The rate of slope change was greater at the higher end of the temperature range. The relation between time to flowering and minimum temperature was more curvilinear that that for maximum temperature except at higher temperatures. Minimum temperatures below 43° F lengthened the time to flowering for the three varieties. Varietal differences appeared to be expressed more by the relation with daily maximum than with daily minimum temperatures. The expressions calculated should be more accurate for prediction purposes than a linear heat unit system, plus they tend to describe the individual responses to changes in minimum and maximum temperatures. A certain lack of fit for the relation still exists, indicating perhaps some other measure, such as solar radiation, should also be included.

Three Lessons on Parabolas—What, Where, Why

2014 ◽  
Vol 108 (5) ◽  
pp. 368-375
Author(s):  
Ben Ceyanes ◽  
Pamela Lockwood ◽  
Kristina Gill
Keyword(s):  
Linear Functions ◽  
Quadratic Functions ◽  
Geometer's Sketchpad

Using The Geometer's Sketchpad, this sequence of algebra lessons introduces quadratic functions as the product of two linear functions.

scholarly journals Linear Coordinate-Descent Message Passing for Quadratic Optimization

2012 ◽  
Vol 24 (12) ◽  
pp. 3340-3370 ◽  
Author(s):  
Guoqiang Zhang ◽  
Richard Heusdens
Keyword(s):  
Message Passing ◽  
Quadratic Optimization ◽  
Coordinate Descent ◽  
Linear Functions ◽  
Quadratic Functions ◽  
General Graph ◽  
Message Passing Algorithm ◽  
Multiple Cycles ◽  
Quadratic Matrix ◽  
Two Parameters

In this letter, we propose a new message-passing algorithm for quadratic optimization. The design of the new algorithm is based on linear coordinate descent between neighboring nodes. The updating messages are in a form of linear functions as compared to the min-sum algorithm of which the messages are in a form of quadratic functions. As a result, the linear coordinate-descent (LiCD) algorithm transmits only one parameter per message as opposed to the min-sum algorithm, which transmits two parameters per message. We show that when the quadratic matrix is walk-summable, the LiCD algorithm converges. By taking the LiCD algorithm as a subroutine, we also fix the convergence issue for a general quadratic matrix. The LiCD algorithm works in either a synchronous or asynchronous message-passing manner. Experimental results show that for a general graph with multiple cycles, the LiCD algorithm has comparable convergence speed to the min-sum algorithm, thereby reducing the number of parameters to be transmitted and the computational complexity.

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