scholarly journals Relational cost analysis in a functional-imperative setting

2021 ◽  
Vol 31 ◽  
Author(s):  
WEIHAO QU ◽  
MARCO GABOARDI ◽  
DEEPAK GARG
Keyword(s):  
Cost Analysis ◽  
Higher Order ◽  
Relative Cost ◽  
Type Checking ◽  
The Difference

Abstract Relational cost analysis aims at formally establishing bounds on the difference in the evaluation costs of two programs. As a particular case, one can also use relational cost analysis to establish bounds on the difference in the evaluation cost of the same program on two different inputs. One way to perform relational cost analysis is to use a relational type-and-effect system that supports reasoning about relations between two executions of two programs. Building on this basic idea, we present a type-and-effect system, called ARel, for reasoning about the relative cost (the difference in the evaluation cost) of array-manipulating, higher order functional-imperative programs. The key ingredient of our approach is a new lightweight type refinement discipline that we use to track relations (differences) between two mutable arrays. This discipline combined with Hoare-style triples built into the types allows us to express and establish precise relative costs of several interesting programs that imperatively update their data. We have implemented ARel using ideas from bidirectional type checking.

A symmetry-preserving difference scheme and analytical solutions of a generalized higher-order beam equation

2021 ◽  
Vol 477 (2255) ◽  
Author(s):  
Shou-Fu Tian ◽  
Mei-Juan Xu ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Vector Fields ◽  
Higher Order ◽  
Beam Equation ◽  
Series Solutions ◽  
Local Conservation ◽  
Power Series Method ◽  
Potential System ◽  
Power Series Solutions ◽  
The Difference

Under investigation in this work is a generalized higher-order beam equation, which is an important physical model and describes the vibrations of a rod. By considering Lie symmetry analysis, and using the power series method, we derive the geometric vector fields, symmetry reductions, group invariant solutions and power series solutions of the equation, respectively. The convergence analysis of the power series solutions are also provided with detailed proof. Furthermore, by virtue of the multipliers, the local conservation laws of the equation are derived as well. Furthermore, an effective and direct approach is proposed to study the symmetry-preserving discretization for the equation via its potential system. Finally, the invariant difference models of the generalized beam equation are successfully constructed. Our results show that it is very useful to construct the difference models of the potential system instead of the original equation.

scholarly journals HOTS (Higher Order Thinking Skill) Based Monopoly Development as Learning Media for Animal and Food Materials

2020 ◽  
Vol 5 (2) ◽  
pp. 83-87
Author(s):  
Rischa Dwi Arianti ◽  
Arfilia Wijayanti ◽  
Filia Prima Artharina
Keyword(s):  
Higher Order Thinking ◽  
Development Stage ◽  
Higher Order ◽  
Research Model ◽  
Thinking Skill ◽  
Food Material ◽  
Implementation Phase ◽  
Class Average ◽  
Evaluation Stage ◽  
The Difference

This research model uses several stages, namely the analysis phase, the design phase, the development stage, the implementation phase, the evaluation stage. The results showed the difference in class average between classes using media and not using monopoly media based on HOTS (Higher Order Thinking Skill). This is evidenced by the results of the t-test in which the number of t arithmetic (3,590)> ttable (1,708). So the result is effectiveness in the use of HOTS (Higher Order Thingking Skill) based animal and food material monopoly in grade IV SD 01 Kalicari.

scholarly journals Improving higher-order thingking skill through POE (Predict, Observe, Explain) and guided discovery learning models

2019 ◽  
Vol 5 (2) ◽  
Author(s):  
Witriyani Suryamiati ◽  
Adi Pasah Kahar ◽  
Anandita Eka Setiadi
Keyword(s):  
Experimental Research ◽  
Higher Order Thinking ◽  
Thinking Skills ◽  
Higher Order ◽  
Discovery Learning ◽  
Learning Models ◽  
Guided Discovery ◽  
Higher Order Thinking Skills ◽  
Quasi Experimental ◽  
The Difference

The low level of students’ higher order thinking skills (HOTS) has been the main problem of education in Indonesia. This study aimed to determine the difference of students’ HOTS taught by using POE and Guided Discovery learning models. This quasi-experimental research involved 34 students of X IPA 3 and 32 students of X IPA 4 at SSHS 1 of Sungai Ambawang as the sample. The data obtained by using test which was analyzed using Mann-Whitney U-test. The results showed that the students’ HOTS who were treated with POE were significantly higher than those who were taught using Guided Discovery learning. Therefore, it is suggested to implement POE to improve students’ HOTS.

From First-Order Coherence to Higher-Order Coherence of Synchrotron Radiation

1998 ◽  
Vol 5 (3) ◽  
pp. 305-308 ◽  
Author(s):  
Tsuneaki Miyahara
Keyword(s):  
Synchrotron Radiation ◽  
Free Electron ◽  
Higher Order ◽  
Second Order ◽  
Free Electron Lasers ◽  
First Order ◽  
Noise Characteristics ◽  
The Difference

The difference between first-order and second-order coherence of synchrotron radiation is discussed in relation to how they can be measured and how they affect the noise characteristics of future free-electron lasers.

Dynamics of a Higher Order Rational Difference Equation

2011 ◽  
Vol 216 ◽  
pp. 50-55 ◽  
Author(s):  
Yi Yang ◽  
Fei Bao Lv
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Initial Conditions ◽  
Higher Order ◽  
Rational Difference Equation ◽  
The Difference

In this paper, we address the difference equation xn=pxn-s+xn-t/q+xn-t n=0,1,... with positive initial conditions where s, t are distinct nonnegative integers, p, q > 0. Our results not only include some previously known results, but apply to some difference equations that have not been investigated so far.

scholarly journals Higher-order Lagrangian perturbative theory for the Cosmic Web

2014 ◽  
Vol 11 (S308) ◽  
pp. 119-120
Author(s):  
Takayuki Tatekawa ◽  
Shuntaro Mizuno
Keyword(s):  
Perturbation Theory ◽  
Fourth Order ◽  
Initial Conditions ◽  
Higher Order ◽  
Order Perturbation ◽  
Initial Condition ◽  
The Difference ◽  
Fifth Order ◽  
The Universe ◽  
Higher Order Lagrangian

AbstractZel'dovich proposed Lagrangian perturbation theory (LPT) for structure formation in the Universe. After this, higher-order perturbative equations have been derived. Recently fourth-order LPT (4LPT) have been derived by two group. We have shown fifth-order LPT (5LPT) In this conference, we notice fourth- and more higher-order perturbative equations. In fourth-order perturbation, because of the difference in handling of spatial derivative, there are two groups of equations. Then we consider the initial conditions for cosmological N-body simulations. Crocce, Pueblas, and Scoccimarro (2007) noticed that second-order perturbation theory (2LPT) is required for accuracy of several percents. We verify the effect of 3LPT initial condition for the simulations. Finally we discuss the way of further improving approach and future applications of LPTs.

Prospective analysis of visual function changes in patients with dermatochalasis after upper eyelid blepharoplasty

2019 ◽  
Vol 30 (5) ◽  
pp. 978-984
Author(s):  
Meryem Altin Ekin ◽  
Seyda Karadeniz Ugurlu
Keyword(s):  
Visual Acuity ◽  
Contrast Sensitivity ◽  
Visual Function ◽  
Spherical Aberration ◽  
Higher Order ◽  
Rank Test ◽  
Higher Order Aberrations ◽  
Upper Eyelid ◽  
Spatial Frequencies ◽  
The Difference

Objective: To evaluate the changes of visual acuity, contrast sensitivity, astigmatism, and higher order aberrations after blepharoplasty in patients with dermatochalasis. Methods: Two hundred six eyelids of 103 patients with dermatochalasis were prospectively studied. Visual acuity, contrast sensitivity, corneal topography, astigmatism degree, and higher order aberrations were examined and recorded before and at 1 month after upper eyelid blepharoplasty. Change in contrast sensitivity and astigmatism values were determined according to margin reflex distance of patients, which were classified into three following groups: <2 mm, 2–3 mm, and ⩾ 4 mm. A Wilcoxon signed rank test was performed to compare the difference. Results: No significant differences were observed for visual acuity (p = 0.157). The contrast sensitivity of patients significantly increased at all spatial frequencies both under glare and nonglare conditions (p < 0.05). The mean refractive astigmatism significantly decreased from ‒1.01 ± 1.3 to ‒0.79 ± 0.71, postoperatively (p = 0.029). In patients with marginal reflex distance < 2 mm, mean contrast sensitivity was increased (p < 0.001) and mean astigmatism was decreased significantly (p < 0.001) compared with those with ⩾ 2 mm. Higher order aberrations decreased significantly from 0.62 ± 0.41 µm to 0.55 ± 0.38 µm (p = 0.038) after blepharoplasty. Root mean square of the vertical trefoil (p = 0.038), vertical coma (p = 0.002), horizontal trefoil (p = 0.027), third-order aberration (p = 0.005), secondary vertical stigmatism (p = 0.001), spherical aberration (p = 0.023), secondary horizontal astigmatism (p = 0.002), fourth-order aberration (p = 0.024), vertical pentafoil (p = 0.015), secondary horizontal coma (p = 0.035), secondary horizontal trefoil (p = 0.030), and horizontal pentafoil (p = 0.048) were decreased significantly. Conclusion: Upper eyelid blepharoplasty in patients with dermatochalasis has a significant improvement in visual function in terms of contrast sensitivity, astigmatism, and higher order aberrations.

A theoretical evaluation of linearity

1993 ◽  
Vol 39 (3) ◽  
pp. 405-413 ◽  
Author(s):  
M H Kroll ◽  
K Emancipator
Keyword(s):  
Higher Order ◽  
Visual Evaluation ◽  
Theoretical Evaluation ◽  
First Order ◽  
First Derivative ◽  
Lack Of Fit ◽  
Linear Polynomial ◽  
Straight Line ◽  
The Difference ◽  
Major Property

Abstract The measure of linearity is an important part of the evaluation of a method. According to the NCCLS guidelines (Document EP6-P), results of a linearity experiment are fit to a straight line and judged linear either by visual evaluation, which is subjective, or by the lack-of-fit test. This approach depends on the precision of the method, is not necessarily conclusive, and fails to be quantitative. We define linearity as a measure of how well a first-order (linear) polynomial fits the data compared with a higher-order (nonlinear) polynomial. The major property of a linear polynomial is that the first derivative is a constant. The nonlinearity of a method can be measured by the difference between these two polynomials (first-order and higher-order) at specific values or, as an average, the root-mean difference. This approach is independent of the precision of the assay and is conclusive, quantitative, and objective.

Sign in / Sign up

Export Citation Format

Share Document