Retractions in Intersection Types

This paper deals with retraction - intended as isomorphic embedding - in intersection types building left and right inverses as terms of a lambda calculus with a bottom constant. The main result is a necessary and sufficient condition two strict intersection types must satisfy in order to assure the existence of two terms showing the first type to be a retract of the second one. Moreover, the characterisation of retraction in the standard intersection types is discussed.Comment: In Proceedings ITRS 2016, arXiv:1702.0187

Gradient type optimization methods for electronic structure calculations

The density functional theory (DFT) in electronic structure calculations can be formulated as either a nonlinear eigenvalue or direct minimization problem. The most widely used approach for solving the former is the so-called self-consistent field (SCF) iteration. A common observation is that the convergence of SCF is not clear theoretically while approaches with convergence guarantee for solving the latter are often not competitive to SCF numerically. In this paper, we study gradient type methods for solving the direct minimization problem by constructing new iterations along the gradient on the Stiefel manifold. Global convergence (i.e., convergence to a stationary point from any initial solution) as well as local convergence rate follows from the standard theory for optimization on manifold directly. A major computational advantage is that the computation of linear eigenvalue problems is no longer needed. The main costs of our approaches arise from the assembling of the total energy functional and its gradient and the projection onto the manifold. These tasks are cheaper than eigenvalue computation and they are often more suitable for parallelization as long as the evaluation of the total energy functional and its gradient is efficient. Numerical results show that they can outperform SCF consistently on many practically large systems.Comment: 24 pages, 11 figures, 59 references, and 1 acknowledgement

Retraction: the “other face” of research collaboration?

The last two decades have witnessed the rising prevalence of both co-publishing and retraction. Focusing on research collaboration, this paper utilizes a unique dataset to investigate factors contributing to retraction probability and elapsed time between publication and retraction. Data analysis reveals that the majority of retracted papers are multi-authored and that repeat offenders are collaboration prone. Yet, all things being equal, collaboration, in and of itself, does not increase the likelihood of producing flawed or fraudulent research, at least in the form of retraction. That holds for all retractions and also retractions due to falsification, fabrication, and plagiarism (FFP). The research also finds that publications with authors from elite universities are less likely to be retracted, which is particularly true for retractions due to FFP. China stands out with the fastest retracting speed compared to other countries. Possible explanations, limitations, and policy implications are also discussed

Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows

This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative ordinary differential equations. This includes Riemannian gradient flow systems which occur naturally in optimization problems. The Itoh--Abe discrete gradient is formulated and applied to gradient systems, yielding a derivative-free optimization algorithm. The algorithm is tested on two eigenvalue problems and two problems from manifold valued imaging: InSAR denoising and DTI denoising.Comment: Post-revision version. To appear in SIAM Journal on Scientific Computin

On the Continuity of Representations of Effectivity Functions.

An effectivity function assigns to each coalition of individuals in a society a family of subsets of alternatives such that the coalition can force the outcome of society’s choice to be a member of each of the subsets separately. A representation of an effectivity function is a game form with the same power structure as that speci?ed by the effectivity function. In the present paper we investigate the continuity properties of the outcome functions of such representation. It is shown that while it is not in general possible to find continuous representations, there are important subfamilies of effectivity functions for which continuous representations exist. Moreover, it is found that in the study of continuous representations one may practically restrict attention to effectivity functions on the Cantor set. Here it is found that general effectivity functions have representations with lower or upper semicontinuous outcome function.

The Kapitza - Dirac effect

The Kapitza - Dirac effect is the diffraction of a well - collimated particle beam by a standing wave of light. Why is this interesting? Comparing this situation to the introductory physics textbook example of diffraction of a laser beam by a grating, the particle beam plays the role of the incoming wave and the standing light wave the role of the material grating, highlighting particle - wave duality. Apart from representing such a beautiful example of particle - wave duality, the diffracted particle beams are coherent. This allows the construction of matter interferometers and explains why the Kapitza - Dirac effect is one of the workhorses in the field of atom optics. Atom optics concerns the manipulation of atomic waves in ways analogous to the manipulation of light waves with optical elements. The excitement and activity in this new field of physics stems for a part from the realisation that the shorter de Broglie wavelengths of matter waves allow ultimate sensitivities for diffractive and interferometric experiments that in principle would far exceed their optical analogues. Not only is the Kapitza - Dirac effect an important enabling tool for this field of physics, but diffraction peaks have never been observed for electrons, for which is was originally proposed in 1933. Why has this not been observed? What is the relation between the interaction of laser light with electrons and the interaction of laser light with atoms, or in other words what is the relation between the ponderomotive potential and the lightshift potential? Would it be possible to build interferometers using the Kapitza - Dirac effect for other particles? These questions will be addressed in this paper.Comment: 17 pages, 13 figure

Intrinsic energy conversion mechanism via telescopic extension and retraction of concentric carbon nanotubes

The conversion of other forms of energy into mechanical work through the geometrical extension and retraction of nanomaterials has a wide variety of potential applications, including for mimicking biomotors. Here, using molecular dynamic simulations, we demonstrate that there exists an intrinsic energy conversion mechanism between thermal energy and mechanical work in the telescopic motions of double-walled carbon nanotubes (DWCNTs). A DWCNT can inherently convert heat into mechanical work in its telescopic extension process, while convert mechanical energy into heat in its telescopic retraction process. These two processes are thermodynamically reversible. The underlying mechanism for this reversibility is that the entropy changes with the telescopic overlapping length of concentric individual tubes. We find also that the entropy effect enlarges with the decreasing intertube space of DWCNTs. As a result, the spontaneously telescopic motion of a condensed DWCNT can be switched to extrusion by rising the system temperature above a critical value. These findings are important for fundamentally understanding the mechanical behavior of concentric nanotubes, and may have general implications in the application of DWCNTs as linear motors in nanodevices