scholarly journals Weak associativity and quasigroup units

2019 ◽  
Vol 105 (119) ◽  
pp. 17-24
Author(s):  
Aleksandar Krapez
Keyword(s):  
Partial Solution ◽  
Middle Unit

We investigate a family of identities similar to weak associativity: x(y/y)?z = x?(y/y)z which might imply the existence of the {left, right, middle} unit in a quasigroup. A partial solution to Krapez, Shcherbacov Problem concerning such identities and consequently to similar well known Belousov's Problem is obtained. Another problem by Krapez and Shcherbacov is solved affirmatively, showing that there are many single identities determining unipotent loops among quasigroups.

Big Questions in Ecology and Evolution

2009 ◽  
Author(s):  
Thomas N. Sherratt ◽  
David M. Wilkinson
Keyword(s):  
Partial Solution ◽  
Fundamental Importance ◽  
Evolutionary Perspective ◽  
Text Book ◽  
Broad Audience ◽  
The Future ◽  
The Tropics ◽  
Made In ◽  
Do So

Why do we age? Why cooperate? Why do so many species engage in sex? Why do the tropics have so many species? When did humans start to affect world climate? This book provides an introduction to a range of fundamental questions that have taxed evolutionary biologists and ecologists for decades. Some of the phenomena discussed are, on first reflection, simply puzzling to understand from an evolutionary perspective, whilst others have direct implications for the future of the planet. All of the questions posed have at least a partial solution, all have seen exciting breakthroughs in recent years, yet many of the explanations continue to be hotly debated. Big Questions in Ecology and Evolution is a curiosity-driven book, written in an accessible way so as to appeal to a broad audience. It is very deliberately not a formal text book, but something designed to transmit the excitement and breadth of the field by discussing a number of major questions in ecology and evolution and how they have been answered. This is a book aimed at informing and inspiring anybody with an interest in ecology and evolution. It reveals to the reader the immense scope of the field, its fundamental importance, and the exciting breakthroughs that have been made in recent years.

scholarly journals Graph Learning for Combinatorial Optimization: A Survey of State-of-the-Art

2021 ◽  
Author(s):  
Yun Peng ◽  
Byron Choi ◽  
Jianliang Xu
Keyword(s):  
Machine Learning ◽  
Combinatorial Optimization ◽  
Graph Embedding ◽  
Partial Solution ◽  
Complex Data ◽  
Learning Methods ◽  
Graph Learning ◽  
Second Stage ◽  
End To End ◽  
Embedding Methods

AbstractGraphs have been widely used to represent complex data in many applications, such as e-commerce, social networks, and bioinformatics. Efficient and effective analysis of graph data is important for graph-based applications. However, most graph analysis tasks are combinatorial optimization (CO) problems, which are NP-hard. Recent studies have focused a lot on the potential of using machine learning (ML) to solve graph-based CO problems. Most recent methods follow the two-stage framework. The first stage is graph representation learning, which embeds the graphs into low-dimension vectors. The second stage uses machine learning to solve the CO problems using the embeddings of the graphs learned in the first stage. The works for the first stage can be classified into two categories, graph embedding methods and end-to-end learning methods. For graph embedding methods, the learning of the the embeddings of the graphs has its own objective, which may not rely on the CO problems to be solved. The CO problems are solved by independent downstream tasks. For end-to-end learning methods, the learning of the embeddings of the graphs does not have its own objective and is an intermediate step of the learning procedure of solving the CO problems. The works for the second stage can also be classified into two categories, non-autoregressive methods and autoregressive methods. Non-autoregressive methods predict a solution for a CO problem in one shot. A non-autoregressive method predicts a matrix that denotes the probability of each node/edge being a part of a solution of the CO problem. The solution can be computed from the matrix using search heuristics such as beam search. Autoregressive methods iteratively extend a partial solution step by step. At each step, an autoregressive method predicts a node/edge conditioned to current partial solution, which is used to its extension. In this survey, we provide a thorough overview of recent studies of the graph learning-based CO methods. The survey ends with several remarks on future research directions.

Hamiltonicity of a class of toroidal graphs

2020 ◽  
Vol 70 (2) ◽  
pp. 497-503
Author(s):  
Dipendu Maity ◽  
Ashish Kumar Upadhyay
Keyword(s):  
Connected Graph ◽  
Hamiltonian Cycle ◽  
Partial Solution ◽  
The Other ◽  
Hamiltonian Cycles ◽  
The Face ◽  
Toroidal Graphs

Abstract If the face-cycles at all the vertices in a map are of same type then the map is said to be a semi-equivelar map. There are eleven types of semi-equivelar maps on the torus. In 1972 Altshuler has presented a study of Hamiltonian cycles in semi-equivelar maps of three types {36}, {44} and {63} on the torus. In this article we study Hamiltonicity of semi-equivelar maps of the other eight types {33, 42}, {32, 41, 31, 41}, {31, 61, 31, 61}, {34, 61}, {41, 82}, {31, 122}, {41, 61, 121} and {31, 41, 61, 41} on the torus. This gives a partial solution to the well known Conjecture that every 4-connected graph on the torus has a Hamiltonian cycle.

scholarly journals Designing a Bonus-Malus system reflecting the claim size under the dependent frequency–severity model

2021 ◽  
pp. 1-25
Author(s):  
Rosy Oh ◽  
Joseph H.T. Kim ◽  
Jae Youn Ahn
Keyword(s):  
Recent Literature ◽  
Insurance Industry ◽  
Random Effect ◽  
Random Effect Model ◽  
Partial Solution ◽  
Risk Classification ◽  
Transition Rule ◽  
Auto Insurance ◽  
Dependent Frequency ◽  
Effect Model

In the auto insurance industry, a Bonus-Malus System (BMS) is commonly used as a posteriori risk classification mechanism to set the premium for the next contract period based on a policyholder's claim history. Even though the recent literature reports evidence of a significant dependence between frequency and severity, the current BMS practice is to use a frequency-based transition rule while ignoring severity information. Although Oh et al. [(2020). Bonus-Malus premiums under the dependent frequency-severity modeling. Scandinavian Actuarial Journal 2020(3): 172–195] claimed that the frequency-driven BMS transition rule can accommodate the dependence between frequency and severity, their proposal is only a partial solution, as the transition rule still completely ignores the claim severity and is unable to penalize large claims. In this study, we propose to use the BMS with a transition rule based on both frequency and size of claim, based on the bivariate random effect model, which conveniently allows dependence between frequency and severity. We analytically derive the optimal relativities under the proposed BMS framework and show that the proposed BMS outperforms the existing frequency-driven BMS. Later, numerical experiments are also provided using both hypothetical and actual datasets in order to assess the effect of various dependencies on the BMS risk classification and confirm our theoretical findings.

scholarly journals Political and Economic Forces Sustaining Social Security

2004 ◽  
Vol 4 (1) ◽  
Author(s):  
Casey B Mulligan ◽  
Xavier Sala-i-Martin
Keyword(s):  
Social Security ◽  
Market Failure ◽  
The Elderly ◽  
Partial Solution ◽  
Companion Paper ◽  
Majority Voting ◽  
Pressure Group ◽  
Intergenerational Redistribution ◽  
Economic Forces ◽  
Political Theories

Abstract What economic forces create and sustain old-age Social Security as a public program? We relate political, efficiency, and narrative theories of Social Security to empirical results reported in our companion paper in this volume. Political theories, including rational majority voting and pressure group theories, feature a redistributive struggle among groups. "Efficiency theories," which model SS as a full or partial solution to market failure, include optimal redistribution, retirement insurance, and alleviating labor market congestion. Finally we analyze three "narrative" theories. Overall, retirement, and not alleviating poverty, seems important at the margin, which means that plans to reduce intergenerational redistribution may not be politically sustainable merely because they provide "adequate" incomes for the elderly. Politics seem important, because cross-cohort redistribution is so prevalent, even when the old are consuming as much or more than do the young. SS reform would therefore be assisted by political reforms equalizing political power across generations.

scholarly journals An Alternative Test of Racial Prejudice in Motor Vehicle Searches: Theory and Evidence

2006 ◽  
Vol 96 (1) ◽  
pp. 127-151 ◽  
Author(s):  
Shamena Anwar ◽  
Hanming Fang
Keyword(s):  
Simple Model ◽  
Motor Vehicle ◽  
Search Behavior ◽  
Partial Solution ◽  
Racial Prejudice ◽  
Omitted Variables ◽  
Alternative Test ◽  
Empirical Tests ◽  
Unique Dataset

We propose a simple model of trooper behavior to design empirical tests for whether troopers of different races are monolithic in their search behavior, and whether they exhibit relative racial prejudice in motor vehicle searches. Our test of relative racial prejudice provides a partial solution to the well-known inframarginality and omitted-variables problems associated with outcome tests. When applied to a unique dataset from Florida, our tests soundly reject the hypothesis that troopers of different races are monolithic in their search behavior, but the tests fail to reject the hypothesis that troopers of different races do not exhibit relative racial prejudice.

Structural and geochronological constraints on the role of partial melting during the formation of the Shuswap metamorphic core complex at the latitude of the Thor-Odin dome, British Columbia

1999 ◽  
Vol 36 (6) ◽  
pp. 917-943 ◽  
Author(s):  
Olivier Vanderhaeghe ◽  
Christian Teyssier ◽  
Richard Wysoczanski
Keyword(s):  
Partial Melting ◽  
Metamorphic Core Complex ◽  
High Grade ◽  
Core Complex ◽  
Genetic Link ◽  
The Core ◽  
Lower Unit ◽  
Geochronological Constraints ◽  
Metamorphic Core ◽  
Middle Unit

At the latitude of the Thor-Odin dome, the Shuswap metamorphic core complex exposes a ~15 km thick structural section composed of an upper unit that preserved Mesozoic metamorphism, structures, and cooling ages, separated from the underlying high-grade rocks by low-angle detachment zones. Below the detachments, the core of the complex consists of an amphibolite-facies middle unit overlying a migmatitic lower unit exposed in the core of the Thor-Odin dome. Combined structural and super high resolution ion microprobe (SHRIMP) U-Pb geochronology studies indicate that the pervasive shallowly dipping foliation and east-west lineation developed in the presence of melt during Paleocene time. SHRIMP analyses of complexly zoned zircon grains suggest that the migmatites of the lower unit crystallized at ~56 Ma, and a syntectonic leucogranite at ~60 Ma. We suggest that leucogranite migrated upward from the migmatites through an array of dikes and sills that permeated the middle unit and ponded to form laccoliths spatially related to the detachment zones. The similarity in ages of inherited zircon cores in the two migmatite and the leucogranite samples suggests a genetic link consistent with the structural analysis. Following the crystallization of migmatites, the terrane cooled rapidly, as indicated by argon thermochronology. We propose that exhumation of the core of the Canadian Cordillera during the formation of the Shuswap metamorphic core complex occurred from ~60 to 56 Ma at a time when the crust was significantly partially molten. These structural and temporal relationships suggest a genetic link between mechanical weakening of the crust by partial melting, late-orogenic collapse, and exhumation of high-grade rocks in the hinterland of a thermally mature orogenic belt.

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