scholarly journals Developing an Optimal Class of Generic Sixteenth-Order Simple-Root Finders and Investigating Their Dynamics

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 8 ◽  
Author(s):  
Young Hee Geum ◽  
Young Ik Kim ◽  
Beny Neta
Keyword(s):  
Global Convergence ◽  
Real World ◽  
Simple Root ◽  
Weight Functions ◽  
Root Finding ◽  
Special Cases ◽  
Attraction Basins ◽  
Visual Description ◽  
Future Work ◽  
Real World Problems

Developed here are sixteenth-order simple-root-finding optimal methods with generic weight functions. Their numerical and dynamical aspects are investigated with the establishment of a main theorem describing the desired optimal convergence. Special cases with polynomial and rational weight functions have been extensively studied for applications to real-world problems. A number of computational experiments clearly support the underlying theory on the local convergence of the proposed methods. In addition, to investigate the relevant global convergence, we focus on the dynamics of the developed methods, as well as other known methods through the visual description of attraction basins. Finally, we summarized the results, discussion, conclusion, and future work.

scholarly journals Automated Facilitation Support in Online Forum

2021 ◽  
Author(s):  
Wen Gu
Keyword(s):  
Real World ◽  
Collective Intelligence ◽  
Case Based Reasoning ◽  
Online Forum ◽  
Promising Application ◽  
The Common ◽  
Future Work ◽  
Level Of Agreement ◽  
Case Based ◽  
Real World Problems

Online forum that gathers participants together to solve the common issues that they are facing is considered as a promising application of utilizing collective intelligence to solve complicated real-world problems. To facilitate the discussions in online forum to proceed smoothly and to build consensus efficiently, human facilitators are introduced into the system. With the increasing sophistication of online forum, human facilitators related problems such as human bias and restricted scale become critical. Therefore, it is critical to explore approaches to support human facilitators in conducting facilitation. However, most of the existing facilitation support techniques only support predefined facilitation tasks that could be defined by static rules. In this research, we aim to explore potential solutions for supporting the human facilitators to conduct facilitation in online forum. As the first step, we have proposed a case-based reasoning (CBR)-based framework that targets support facilitation by utilizing past successful facilitation experience. Currently, our work is focusing on the specific facilitation task of detecting influential user in the online forum. In the future work, we are planning to propose approaches of solving other specific facilitation tasks such as measuring the level of agreement and encouraging participants to reach a consensus.

scholarly journals Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity

2019 ◽  
Vol 33 ◽  
pp. 1877-1884 ◽  
Author(s):  
John P. Dickerson ◽  
Karthik Abinav Sankararaman ◽  
Aravind Srinivasan ◽  
Pan Xu
Keyword(s):  
Real World ◽  
The Other ◽  
Objective Functions ◽  
Bipartite Matching ◽  
Matching Problems ◽  
Special Cases ◽  
Coverage Function ◽  
Synthetic Datasets ◽  
Novel Algorithms ◽  
Real World Problems

In bipartite matching problems, vertices on one side of a bipartite graph are paired with those on the other. In its online variant, one side of the graph is available offline, while the vertices on the other side arrive online. When a vertex arrives, an irrevocable and immediate decision should be made by the algorithm; either match it to an available vertex or drop it. Examples of such problems include matching workers to firms, advertisers to keywords, organs to patients, and so on. Much of the literature focuses on maximizing the total relevance—modeled via total weight—of the matching. However, in many real-world problems, it is also important to consider contributions of diversity: hiring a diverse pool of candidates, displaying a relevant but diverse set of ads, and so on. In this paper, we propose the Online Submodular Bipartite Matching (OSBM) problem, where the goal is to maximize a submodular function f over the set of matched edges. This objective is general enough to capture the notion of both diversity (e.g., a weighted coverage function) and relevance (e.g., the traditional linear function)—as well as many other natural objective functions occurring in practice (e.g., limited total budget in advertising settings). We propose novel algorithms that have provable guarantees and are essentially optimal when restricted to various special cases. We also run experiments on real-world and synthetic datasets to validate our algorithms.

scholarly journals A Generic Family of Optimal Sixteenth-Order Multiple-Root Finders and Their Dynamics Underlying Purely Imaginary Extraneous Fixed Points

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 562 ◽  
Author(s):  
Min-Young Lee ◽  
Young Ik Kim ◽  
Beny Neta
Keyword(s):  
Fixed Points ◽  
Multiple Root ◽  
Weight Functions ◽  
Computational Results ◽  
Special Cases ◽  
Extraneous Fixed Points ◽  
Free Parameters ◽  
Future Work ◽  
Generic Family ◽  
Selection Of

A generic family of optimal sixteenth-order multiple-root finders are theoretically developed from general settings of weight functions under the known multiplicity. Special cases of rational weight functions are considered and relevant coefficient relations are derived in such a way that all the extraneous fixed points are purely imaginary. A number of schemes are constructed based on the selection of desired free parameters among the coefficient relations. Numerical and dynamical aspects on the convergence of such schemes are explored with tabulated computational results and illustrated attractor basins. Overall conclusion is drawn along with future work on a different family of optimal root-finders.

scholarly journals Handrails through the Swamp? A Pilot to Test the Integration and Implementation Science Framework in Complex Real-World Research

2021 ◽  
Vol 13 (10) ◽  
pp. 5491
Author(s):  
Melissa Robson-Williams ◽  
Bruce Small ◽  
Roger Robson-Williams ◽  
Nick Kirk
Keyword(s):  
Pilot Study ◽  
Case Studies ◽  
Implementation Science ◽  
Real World ◽  
Environmental Problems ◽  
Environmental Research ◽  
Integrative Framework ◽  
The World ◽  
Science Framework ◽  
Real World Problems

The socio-environmental challenges the world faces are ‘swamps’: situations that are messy, complex, and uncertain. The aim of this paper is to help disciplinary scientists navigate these swamps. To achieve this, the paper evaluates an integrative framework designed for researching complex real-world problems, the Integration and Implementation Science (i2S) framework. As a pilot study, we examine seven inter and transdisciplinary agri-environmental case studies against the concepts presented in the i2S framework, and we hypothesise that considering concepts in the i2S framework during the planning and delivery of agri-environmental research will increase the usefulness of the research for next users. We found that for the types of complex, real-world research done in the case studies, increasing attention to the i2S dimensions correlated with increased usefulness for the end users. We conclude that using the i2S framework could provide handrails for researchers, to help them navigate the swamps when engaging with the complexity of socio-environmental problems.

scholarly journals Combined Games with Randomly Delayed Beginnings

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 534
Author(s):  
F. Thomas Bruss
Keyword(s):  
Discrete Time ◽  
Real World ◽  
Optimal Stopping ◽  
Random Variables ◽  
Approximate Solutions ◽  
Real World Problems

This paper presents two-person games involving optimal stopping. As far as we are aware, the type of problems we study are new. We confine our interest to such games in discrete time. Two players are to chose, with randomised choice-priority, between two games G1 and G2. Each game consists of two parts with well-defined targets. Each part consists of a sequence of random variables which determines when the decisive part of the game will begin. In each game, the horizon is bounded, and if the two parts are not finished within the horizon, the game is lost by definition. Otherwise the decisive part begins, on which each player is entitled to apply their or her strategy to reach the second target. If only one player achieves the two targets, this player is the winner. If both win or both lose, the outcome is seen as “deuce”. We motivate the interest of such problems in the context of real-world problems. A few representative problems are solved in detail. The main objective of this article is to serve as a preliminary manual to guide through possible approaches and to discuss under which circumstances we can obtain solutions, or approximate solutions.

Review of Network Flow Algorithms David P. Williamson

2021 ◽  
Vol 52 (1) ◽  
pp. 12-15
Author(s):  
S.V. Nagaraj
Keyword(s):  
Graduate Students ◽  
Real World ◽  
Network Flow ◽  
Network Flows ◽  
Optimization Problems ◽  
Capacity Constraints ◽  
Incoming Flow ◽  
Network Flow Problems ◽  
Flow Problems ◽  
Real World Problems

This book is on algorithms for network flows. Network flow problems are optimization problems where given a flow network, the aim is to construct a flow that respects the capacity constraints of the edges of the network, so that incoming flow equals the outgoing flow for all vertices of the network except designated vertices known as the source and the sink. Network flow algorithms solve many real-world problems. This book is intended to serve graduate students and as a reference. The book is also available in eBook (ISBN 9781316952894/US$ 32.00), and hardback (ISBN 9781107185890/US$99.99) formats. The book has a companion web site www.networkflowalgs.com where a pre-publication version of the book can be downloaded gratis.

Help communities solve real-world problems with AI

AI Matters ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 12-14
Author(s):  
Tara Chklovski
Keyword(s):  
Real World ◽  
Real World Problems
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