Book chapter
Кластерная модификация метода сопряженных взаимодействий для решения задачи распределения ресурсов в реальном масштабе времени
In this paper we describe the cluster modification for the method of conjugated interactions for resource allocation in real time. In contrast to the original method, this modification allows to guarantee an arbitrarily high stability of the structure of resource allocation regardless of the volatile context of solving the problem.
In book
One of the goals of the first edition of this book back in 2005 was to present a coherent theory for K-Means partitioning and Ward hierarchical clustering. This theory leads to effective data pre-processing options, clustering algorithms and interpretation aids, as well as to firm relations to other areas of data analysis. The goal of this second edition is to consolidate, strengthen and extend this island of understanding in the light of recent developments. Moreover, the material on validation and interpretation of clusters is updated with a system better reflecting the current state of the art and with our recent ``lifting in taxonomies'' approach. The structure of the book has been streamlined by adding two Chapters: ``Similarity Clustering'' and ``Validation and Interpretation'', while removing two chapters: ``Different Clustering Approaches'' and ``General Issues.'' The Chapter on Mathematics of the data recovery approach, in a much extended version, almost doubled in size, now concludes the book. Parts of the removed chapters are integrated within the new structure. The change has added a hundred pages and a couple of dozen examples to the text and, in fact, transformed it into a different species of a book. In the first edition, the book had a Russian doll structure, with a core and a couple of nested shells around. Now it is a linear structure presentation of the data recovery clustering.
Topic 2. Formalized surveys of enterprises top-managers: a tool for evaluations based on qualitative information The second topic of the lecture course «Firm-level Empirical Surveys: Tools and Practice» is presented in this issue. The topic describes possibilities and practice of application of formalized top-managers surveys to studies of enterprises economic behavior. The main attention is focused on development of surveys methodology and tools, and technology of their conducting. Limitations and advantages of surveys and distortion of their data characterizing enterprises state behavior are discussed.
The maximum Nash welfare (MNW) solution — which selects an allocation that maximizes the product of utilities — is known to provide outstanding fairness guarantees when allocating divisible goods. And while it seems to lose its luster when applied to indivisible goods, we show that, in fact, the MNW solution is unexpectedly, strikingly fair even in that setting. In particular, we prove that it selects allocations that are envy free up to one good — a compelling notion that is quite elusive when coupled with economic efficiency. We also establish that the MNW solution provides a good approximation to another popular (yet possibly infeasible) fairness property, the maximin share guarantee, in theory and — even more so — in practice. While finding the MNW solution is computationally hard, we develop a nontrivial implementation, and demonstrate that it scales well on real data. These results lead us to believe that MNW is the ultimate solution for allocating indivisible goods, and underlie its deployment on a popular fair division website.