5,918 research outputs found
Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge
We compute asymptotics for Hankel determinants and orthogonal polynomials
with respect to a discontinuous Gaussian weight, in a critical regime where the
discontinuity is close to the edge of the associated equilibrium measure
support. Their behavior is described in terms of the Ablowitz-Segur family of
solutions to the Painlev\'e II equation. Our results complement the ones in
[Xu,Zhao,2011]. As consequences of our results, we conjecture asymptotics for
an Airy kernel Fredholm determinant and total integral identities for
Painlev\'e II transcendents, and we also prove a new result on the poles of the
Ablowitz-Segur solutions to the Painlev\'e II equation. We also highlight
applications of our results in random matrix theory.Comment: 35 pages, 4 figure
Improving Prolog programs: Refactoring for Prolog
Refactoring is an established technique from the object-oriented (OO)
programming community to restructure code: it aims at improving software
readability, maintainability and extensibility. Although refactoring is not
tied to the OO-paradigm in particular, its ideas have not been applied to Logic
Programming until now.
This paper applies the ideas of refactoring to Prolog programs. A catalogue
is presented listing refactorings classified according to scope. Some of the
refactorings have been adapted from the OO-paradigm, while others have been
specifically designed for Prolog. The discrepancy between intended and
operational semantics in Prolog is also addressed by some of the refactorings.
In addition, ViPReSS, a semi-automatic refactoring browser, is discussed and
the experience with applying ViPReSS to a large Prolog legacy system is
reported. The main conclusion is that refactoring is both a viable technique in
Prolog and a rather desirable one.Comment: To appear in Theory and Practice of Logic Programming (TPLP
A Future of Failure? The Flow of Technology Talent into Government and Civil Society
This report is an evaluation of the technology talent landscape shows a severe paucity of individuals with technical skills in computer science, data science, and the Internet or other information technology expertise in civil society and government. It investigates broadly the health of the talent pipeline that connects individuals studying or working in information technology-related disciplines to careers in public sector and civil society institutions. Barriers to recruitment and retention of individuals with the requisite skills include compensation, a perceived inability to pursue groundbreaking work, and cultural aversion to innovation
Virasoro Constraints for Toric Bundles
We show that the Virasoro conjecture in Gromov--Witten theory holds for the
the total space of a toric bundle if and only if it holds for the
base . The main steps are: (i) we establish a localization formula that
expresses Gromov--Witten invariants of , equivariant with respect to the
fiberwise torus action, in terms of genus-zero invariants of the toric fiber
and all-genus invariants of ; and (ii) we pass to the non-equivariant limit
in this formula, using Brown's mirror theorem for toric bundles.Comment: 24 page
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