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Diaconescu R.,Simion Stoilow Institute of Mathematics
Theoretical Computer Science | Year: 2012

In this paper we develop an axiomatic approach to structured specifications in which both the underlying logical system and corresponding institution of the structured specifications are treated as abstract institutions, which means two levels of institution independence. This abstract axiomatic approach provides a uniform framework for the study of structured specifications independently from any actual choice of specification building operators, and moreover it unifies the theory and the model oriented approaches. Within this framework we develop concepts and results about 'abstract structured specifications' such as co-limits, model amalgamation, compactness, interpolation, sound and complete proof theory, and pushout-style parameterization with sharing, all of them in a top down manner dictated by the upper level of institution independence. © 2012 Elsevier B.V. All rights reserved.


Diaconescu R.,Simion Stoilow Institute of Mathematics
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2014

We survey two important distinctive features of CafeOBJ, namely behavioural specification based upon coherent hidden algebra and heterogeneous specification based upon Grothendieck institutions. Both of them represent seminal contributions to formal specification culture that go much beyond the realm of CafeOBJ. Our presentation includes rather detailed explanations of the motivations and of the process leading to the inception of these concepts and theories. The paper is dedicated to Professor Kokichi Futatsugi, the leader of the CafeOBJ project, and also close friend and collaborator, on the occasion of his retirement. © 2014 Springer-Verlag Berlin Heidelberg.


Negut A.,Massachusetts Institute of Technology | Negut A.,Simion Stoilow Institute of Mathematics
Letters in Mathematical Physics | Year: 2016

We prove the connection between the Nekrasov partition function of (Formula presented.) super-symmetric U(2) gauge theory with adjoint matter and conformal blocks for the Virasoro algebra, as predicted by the Alday–Gaiotto–Tachikawa relations. Mathematically, this is achieved by relating the Carlsson–Okounkov Ext vector bundle on the moduli space of rank 2 sheaves with Liouville vertex operators. Our approach is geometric in nature, and uses a new method for intersection-theoretic computations of the Ext operator. © 2016 Springer Science+Business Media Dordrecht


Ilyashenko Yu.,Cornell University | Ilyashenko Yu.,Moscow State University | Negut A.,Princeton University | Negut A.,Simion Stoilow Institute of Mathematics
Nonlinearity | Year: 2010

This paper deals with attractors of generic dynamical systems. We introduce the notion of ε-invisible set, which is an open set of the phase space in which almost all orbits spend on average a fraction of time no greater than ε. For extraordinarily small values of ε (say, smaller than 2 -100), these are large neighbourhoods of some parts of the attractors in the phase space which an observer virtually never sees when following a generic orbit. For any n ≥ 100, we construct a set Qn in the space of skew products over a solenoid with the fibre a circle having the following properties. Any map from Qn is a structurally stable diffeomorphism; the Lipschitz constants of the map and its inverse are no greater than L (where L is a universal constant that does not depend on n, say L < 100). Moreover, any map from Qn has a 2-n-invisible part of its attractor, whose size is comparable to that of the whole attractor. The set Qn is a ball of radius O(n-2) in the space of skew products with the C1 metric. It consists of structurally stable skew products. Small perturbations of these skew products in the space of all diffeomorphisms still have attractors with the same properties. Thus for all such perturbations, a sizable portion of the attractor is almost never visited by generic orbits and is practically never seen by the observer. © 2010 IOP Publishing Ltd & London Mathematical Society.


Diaconescu R.,Simion Stoilow Institute of Mathematics
Information and Computation | Year: 2011

We develop a general logic-independent structural induction proof method at the level of abstract institutions. This provides a solid and uniform mathematical foundation to induction proof methodologies for a wide variety of actual logic-based formal specification frameworks. Our development is based technically upon an axiomatic approach to substitutions within institution theory. © 2011 Elsevier Inc.

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