This paper examines the fundamental problem of identifying most important nodes in a network. To date, more than hundred centrality measures have been proposed, each evaluating position node network from different perspective. Our work focuses on PageRank which is one computer science used wide range scientific applications. build theoretical foundation for choosing (or rejecting) specific sett...

In a framework with two parties, deterministic voter preferences and geographical constraints, we propose a set of simple axioms and show that they jointly characterize the districting rule that maximizes the number of districts a party can win, given an electoral outcome (the " optimal gerrymandering rule "). As a corollary, we obtain that no districting rule can satisfy our axioms and treat p...

Those of us who pursue neuroeconomic research do so in the belief that neurobiological and decision theoretic research will prove highly complementary. The hoped for complementarities rest in part on the fact that model-building and quantification are as highly valued within neuroscience as they are in economics. Yet methodological tensions remain. In particular, the ‘axiomatic’ modeling method...

It is widely accepted that no amount of robust optimization at the detailed design level can succeed if the design concept itself is flawed (does not satisfy all functional requirements). The author has specifically focused on DFSS deployment in his company in the area of concept generation. Integration of Axiomatic Design has been the most critical element of this improvement. This paper descr...

The purpose of this study is to analyze the set structure of the balance sheet and assets-claims on assets relationship, considering the dual concept of monetary units, the axiomatic theory and accountingspecific axioms. The structure of the balance sheet and assets-claims on assets relationship are examined using a rationalistic, analytical and deductive method; this method uses the axiomatic ...

We report our experiments in TREC 2009 Million Query track and Adhoc task of Web track. Our goal is to evaluate the effectiveness of axiomatic retrieval models on the large data collection. Axiomatic approaches to information retrieval have been recently proposed and studied. The basic idea is to search for retrieval functions that can satisfy all the reasonable retrieval constraints. Previous ...

In the “little theories” version of the axiomatic method, different portions of mathematics are developed in various different formal axiomatic theories. Axiomatic theories may be related by inclusion or by theory interpretation. We argue that the little theories approach is a desirable way to formalize mathematics, and we describe how imps, an Interactive Mathematical Proof System, supports it.

We study the enrichment of models of axiomatic domain theory. To this end, we introduce a new and broader notion of domain, viz. that of complete cuboidal set, that complies with the axiomatic requirements. We show that the category of complete cuboidal sets provides a general notion of enrichment for a wide class of axiomatic domain-theoretic structures.