Keshav Srinivasan

A new world order is taking shape. In the after-math of the World Wars and the Cold War, optimists hoped that the multilateral system envisaged by the UN Charter could finally be realized. Now this vision appears utopian. International cooperation based on a commitment to constitutional government, human rights and the rule of laws was a product of eighteenth century Enlightenment and underwritten first by the European great powers and then by the United States. How will it survive the decline of the predominance of the USA and the rise of new power centres in this century?

Computability theory is the mathematical theory of algorithms, which explores the power and limitations of computation. Classical computability theory formalized the intuitive notion of an algorithm and provided a theoretical basis for digital computers. It also demonstrated the limitations of algorithms and showed that most sets of natural numbers and the problems they encode are not decidable (Turing computable). Important results of modern computability theory include the classification of the computational difficulty of sets and problems. Arithmetical and hyperarithmetical hierarchies and the Turing degrees provide important measures of the level of such difficulty. There are uncountably many Turing degrees and they are partially ordered. These classifications are used in contemporary research to investigate the complexity of problems in modern computable mathematics, for example, regarding structures and their properties.

A cohesive power of a structure is an effective analog of the classical ultrapower of a structure. We start with a computable structure, and consider its effective power over a cohesive set of natural numbers. A cohesive set is an infinite set of natural numbers that is indecomposable with respect to computably enumerable sets. It plays the role of an ultrafilter, and the elements of a cohesive power are the equivalence classes of certain partial computable functions determined by the cohesive set. Thus, unlike many classical ultrapowers, a cohesive power is a countable structure. In this paper we focus on cohesive powers of graphs, equivalence structures, and computable structures with a single unary function satisfying various properties, which can also be viewed as directed graphs. For these computable structures, we investigate the isomorphism types of their cohesive powers, as well as the properties of cohesive powers when they are not isomorphic to the original structure.

The return of individual research results and incidental findings from biobanking research is a much debated ethical issue globally but has extensive relevance in India where the burden of out of pocket health care expenses is high for the majority. The views of 21 ethics committee (EC) members and 22 researchers from Bengaluru, India, concerning the ethics of biobanking research were sought through in‐depth interviews using an unfolding case vignette with probes. A shared view among most was that individual research results which are ‘actionable’ or have ‘clinical significance’ should be returned to the sample contributors through their treating physicians. This was seen as an ethical obligation and a moral duty on the side of the researcher to “give back” to the person who contributed to the research. The challenges foreseen were that of resources, both financial and personnel, for the time and counseling needed to accompany the disclosure of results. Perceptions of ‘ownership’ appear to influence the concept of benefit sharing. While benefit sharing in financial terms was considered ethically challenging, certain researchers and ethics committee members made a case for “two way altruism” where the researcher in return for the altruistic ‘valuable contribution’, shares with the contributor/ community, benefits of the research which could include research findings, improved patient care, and more affordable access to the new diagnostic tests or products arising from the research. This defines the emerging ethic of “giving back” which goes beyond individual rights and ensures reciprocity and distributive justice.