Application of Newton iterative process in approximation of fractional differentiator and integrator

2019 ◽  
Author(s):  
Nitisha Shrivastava ◽  
Pragya Varshney
Keyword(s):  
Iterative Process ◽  
Fractional Differentiator

Bayesian Applications in Auditory Research

2019 ◽  
Vol 62 (3) ◽  
pp. 577-586 ◽  
Author(s):  
Garnett P. McMillan ◽  
John B. Cannon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Interim Analysis ◽  
Iterative Process ◽  
Bayes Theorem ◽  
Sound Therapy ◽  
The Many ◽  
Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

Identifying changes in trends in the age standardized incidence of melanoma in Australia

2019 ◽  
Vol 3 (4) ◽  
pp. 250-252 ◽  
Author(s):  
David M Hille
Keyword(s):  
Public Health ◽  
Linear Regression ◽  
Iterative Process ◽  
Linear Trend ◽  
Piecewise Linear ◽  
Health Issue ◽  
Public Health Issue ◽  
Piecewise Linear Regression ◽  
Significant Public Health ◽  
Males And Females

ObjectiveTo identify changes in the linear trend of the age-standardized incidence of melanoma in Australia for all persons, males, and females. MethodsA two-piece piecewise linear regression was fitted to the data. The piecewise breakpoint varied through an iterative process to determine the model that best fits the data.ResultsStatistically significant changes in the trendof the age-standardized incidence of melanoma in Australia were found for all persons, males, and females. The optimal breakpoint for all persons and males was at 1998. For females, the optimal breakpoint was at 2005. The trend after these breakpoints was flatter than prior to the breakpoints, but still positive.ConclusionMelanoma is a significant public health issue in Australia. Overall incidence continues to increase. However, the rate at which the incidence is increasing appears to be decreasing.

DESIGN APPROACH TO REHABILITATION: DEVELOPING THERAPY ASSISTIVE PRODUCTS FOR CHILDREN WITH HEMIPLEGIC CEREBRAL PALSY

2018 ◽  
Vol 12 (2) ◽  
pp. 307
Author(s):  
G.Y.A. Shanya I. Perera ◽  
W.M.N. Dilshani Ranasinghe
Keyword(s):  
Cerebral Palsy ◽  
Functional Outcomes ◽  
Iterative Process ◽  
Participatory Design ◽  
Design Methodology ◽  
Physical Disabilities ◽  
Comprehensive Understanding ◽  
Constructive Feedback ◽  
Children With Disability ◽  
Hemiplegic Cerebral Palsy

Therapy plays an important role in rehabilitation of children suffering from physical disabilities. Disability conditions like Hemiplegic Cerebral Palsy require vigorous therapy measures, which could be unappealing to children. Using therapy assistive products for rehabilitation can make therapy activities engaging and appealing to children and yield effective outcomes. However, there is limited availability of context based therapy assistive products, which are engaging, and appealing to children suffering from Hemiplegic Cerebral Palsy. This study explores how design methodology can be used to develop therapy assistive products for rehabilitation of children with disability. The study is based on developing a set of therapy assistive products to improve the hand-skills of children with Hemiplegic Cerebral Palsy. Developing therapy assistive products require comprehensive understanding of therapeutic aspects, design aspects and careful integration of the two disciplines. Hence, practicing multidisciplinary and participatory design approaches in the design process is imperative. Usability of therapy assistive products are highly impactive in nature, and therefore an iterative process of prototyping, testing, receiving constructive feedback and developing the products based on feedback should be adopted to achieve feasible and  functional outcomes.

scholarly journals An Energy-Based Discrete Element Modeling Method Coupled with Time-Series Analysis for Investigating Deformations and Failures of Jointed Rock Slopes

2021 ◽  
Vol 11 (12) ◽  
pp. 5447
Author(s):  
Xiaona Zhang ◽  
Gang Mei ◽  
Ning Xi ◽  
Ziyang Liu ◽  
Ruoshen Lin
Keyword(s):  
Time Series ◽  
Iterative Process ◽  
Discrete Element ◽  
Jointed Rock ◽  
Modeling Method ◽  
Discrete Element Modeling ◽  
Rock Slopes ◽  
Sliding Surface ◽  
Element Modeling ◽  
Displacement Based

The discrete element method (DEM) can be effectively used in investigations of the deformations and failures of jointed rock slopes. However, when to appropriately terminate the DEM iterative process is not clear. Recently, a displacement-based discrete element modeling method for jointed rock slopes was proposed to determine when the DEM iterative process is terminated, and it considers displacements that come from rock blocks located near the potential sliding surface that needs to be determined before the DEM modeling. In this paper, an energy-based discrete element modeling method combined with time-series analysis is proposed to investigate the deformations and failures of jointed rock slopes. The proposed method defines an energy-based criterion to determine when to terminate the DEM iterative process in analyzing the deformations and failures of jointed rock slopes. The novelty of the proposed energy-based method is that, it is more applicable than the displacement-based method because it does not need to determine the position of the potential sliding surface before DEM modeling. The proposed energy-based method is a generalized form of the displacement-based discrete element modeling method, and the proposed method considers not only the displacement of each block but also the weight of each block. Moreover, the computational cost of the proposed method is approximately the same as that of the displacement-based discrete element modeling method. To validate that the proposed energy-based method is effective, the proposed method is used to analyze a simple jointed rock slope; the result is compared to that achieved by using the displacement-based method, and the comparative results are basically consistent. The proposed energy-based method can be commonly used to analyze the deformations and failures of general rock slopes where it is difficult to determine the obvious potential sliding surface.

Opinion Dynamics Optimization by Varying Susceptibility to Persuasion via Non-Convex Local Search

2021 ◽  
Vol 16 (2) ◽  
pp. 1-34
Author(s):  
Rediet Abebe ◽  
T.-H. HUBERT Chan ◽  
Jon Kleinberg ◽  
Zhibin Liang ◽  
David Parkes ◽  
...  
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Iterative Process ◽  
Large Scale ◽  
Opinion Dynamics ◽  
Theoretical Models ◽  
Global Optimum ◽  
Local Optimum ◽  
Opinion Formation ◽  
Long Line

A long line of work in social psychology has studied variations in people’s susceptibility to persuasion—the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people’s intrinsic opinions, it is also natural to consider interventions that modify people’s susceptibility to persuasion. In this work, motivated by this fact, we propose an influence optimization problem. Specifically, we adopt a popular model for social opinion dynamics, where each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; agents influence one another’s opinions through an iterative process. Under certain conditions, this iterative process converges to some equilibrium opinion vector. For the unbudgeted variant of the problem, the goal is to modify the resistance of any number of agents (within some given range) such that the sum of the equilibrium opinions is minimized; for the budgeted variant, in addition the algorithm is given upfront a restriction on the number of agents whose resistance may be modified. We prove that the objective function is in general non-convex. Hence, formulating the problem as a convex program as in an early version of this work (Abebe et al., KDD’18) might have potential correctness issues. We instead analyze the structure of the objective function, and show that any local optimum is also a global optimum, which is somehow surprising as the objective function might not be convex. Furthermore, we combine the iterative process and the local search paradigm to design very efficient algorithms that can solve the unbudgeted variant of the problem optimally on large-scale graphs containing millions of nodes. Finally, we propose and evaluate experimentally a family of heuristics for the budgeted variant of the problem.

scholarly journals A Characterization of the Dynamics of Schröder’s Method for Polynomials with Two Roots

2021 ◽  
Vol 5 (1) ◽  
pp. 25
Author(s):  
Víctor Galilea ◽  
José M. Gutiérrez
Keyword(s):  
Nonlinear Equations ◽  
Complex Plane ◽  
Iterative Process ◽  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
Schröder’S Method

The purpose of this work is to give a first approach to the dynamical behavior of Schröder’s method, a well-known iterative process for solving nonlinear equations. In this context, we consider equations defined in the complex plane. By using topological conjugations, we characterize the basins of attraction of Schröder’s method applied to polynomials with two roots and different multiplicities. Actually, we show that these basins are half-planes or circles, depending on the multiplicities of the roots. We conclude our study with a graphical gallery that allow us to compare the basins of attraction of Newton’s and Schröder’s method applied to some given polynomials.

scholarly journals How to measure fluctuating impairments in people with MS: development of an ambulatory assessment version of the EQ-5D-5L in an exploratory study

2021 ◽  
Author(s):  
Christine Blome ◽  
Jill Carlton ◽  
Christoph Heesen ◽  
Mathieu F. Janssen ◽  
Andrew Lloyd ◽  
...  
Keyword(s):  
Exploratory Study ◽  
Iterative Process ◽  
Face Validity ◽  
Ambulatory Assessment ◽  
Standard Assessment ◽  
Before And After ◽  
Standard Paper ◽  
Subsequent Wave ◽  
Patients Perspective ◽  
Time Point

Abstract Background Health fluctuations even within a single day are typical in multiple sclerosis (MS), but are not captured by widely used questionnaires like the EQ-5D-5L. This exploratory study aimed to develop an ambulatory assessment (AA) version of the EQ-5D-5L (EQ-5D-AA) where patients rate their health on mobile phones multiple times per day over several days, and to assess its feasibility and face validity. Methods An initial EQ-5D-AA version was based on two patient focus groups. It was then tested and continuously developed in an iterative process: patients completed it over several days, followed by debriefing interviews. Findings were used to refine the EQ-5D-AA, with the resulting version being tested by the subsequent wave of patients until participants declared no need for changes anymore. Before and after the AA period, participants completed the standard paper-based EQ-5D-5L asking about ‘today’. Results Focus group participants reported that their impairments often fluctuated between and within days. They regarded an AA with three assessments per day over seven days most appropriate; assessment should be retrospective to the previous assessment, but not all items should be assessed at each time point. Four waves of AA testing were conducted. Thirteen out of the 17 participants preferred the AA over standard assessment as they regarded it more informative, but not too burdensome. Conclusion The newly developed one-week AA of the EQ-5D-5L captures within-day and day-to-day health fluctuations in people with MS. From the patients’ perspective, it is a feasible and face valid way to provide important information beyond what is captured by the standard EQ-5D-5L.

scholarly journals Engaging young people in the design of a sexual reproductive health intervention: Lessons learnt from the Yathu Yathu (“For us, by us”) formative study in Zambia

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Melvin Simuyaba ◽  
Bernadette Hensen ◽  
Mwelwa Phiri ◽  
Chisanga Mwansa ◽  
Lawrence Mwenge ◽  
...  
Keyword(s):  
Young People ◽  
Reproductive Health ◽  
Iterative Process ◽  
Service Use ◽  
Service Providers ◽  
Peer Pressure ◽  
Post Exposure Prophylaxis ◽  
Community Based ◽  
Research Activities ◽  
Lessons Learnt

Abstract Background Meeting the sexual and reproductive health (SRH) needs of adolescents and young people (AYP) requires their meaningful engagement in intervention design. We describe an iterative process of engaging AYP to finalise the design of a community-based, peer-led and incentivised SRH intervention for AYP aged 15–24 in Lusaka and the lessons learnt. Methods Between November 2018 and March 2019, 18 focus group discussions, eight in-depth interviews and six observations were conducted to assess AYP’s knowledge of HIV/SRH services, factors influencing AYP’s sexual behaviour and elicit views on core elements of a proposed intervention, including: community-based spaces (hubs) for service delivery, type of service providers and incentivising service use through prevention points cards (PPC; “loyalty” cards to gain points for accessing services and redeem these for rewards). A total of 230 AYP (15 participated twice in different research activities) and 21 adults (only participated in the community mapping discussions) participated in the research. Participants were purposively selected based on age, sex, where they lived and their roles in the study communities. Data were analysed thematically. Results Alcohol and drug abuse, peer pressure, poverty, unemployment and limited recreation facilities influenced AYP’s sexual behaviours. Adolescent boys and young men lacked knowledge of contraceptive services and all AYP of pre and post exposure prophylaxis for HIV prevention. AYP stated a preference for accessing services at “hubs” located in the community rather than the health facility. AYP considered the age, sex and training of the providers when choosing whom they were comfortable accessing services from. PPCs were acceptable among AYP despite the loyalty card concept being new to them. AYP suggested financial and school support, electronic devices, clothing and food supplies as rewards. Conclusions Engaging AYP in the design of an SRH intervention was feasible, informative and considered responsive to their needs. Although AYP’s suggestions were diverse, the iterative process of AYP engagement facilitated the design of an intervention that is informed by AYP and implementable. Trial registration This formative study informed the design of this trial: ClinicalTrials.gov, NCT04060420. Registered 19 August, 2019.

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